_____________________________________________________________________________________________________________

Workshop 2016

“Modeling and Computation of Shocks and Interfaces”

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie, Paris

Organizers

 Philippe G. LeFloch (Paris)

 Charalambos Makridakis  (Brighton)

Supported by the ModCompShock ITN project


 Dec. 6 around 1:30pm to Dec. 8 around 1pm


Main speakers

Remi Abgrall (Zurich)

Benjamin Boutin (Rennes)

Christophe Chalons (Versailles)

Sergey Gavrilyuk (Marseille)

Charalambos Makridakis (Brighton)

Pierangelo Marcati (L’Aquila)

Siddhartha Mishra (Zurich)

Carlos Pares (Malaga)

Nils Risebro (Oslo)

Giovanni Russo (Catania)

Lev Truskinovsky (Palaiseau)

 


Titles of the lectures

Remi Abgrall

Benjamin Boutin Numerical boundary layers for linear hyperbolic IBVP and semigroup estimate

Christophe Chalons On the computation of non conservative products and cell averages in finite volume methods

Makridakis Charalambos  Energy/entropy consistent computational methods

Sergey Gavrilyuk Shock-droplet interaction via a new hyperbolic phase field model

Pierangelo Marcati Splash singularities for incompressible viscoelatic fluids 

Siddhartha Mishra Statistical solutions of systems of conservation laws

Carlos Pares Entropy stable schemes for degenerate convection-diffusion equations

Nils Risebro  Numerical methods for scalar conservation laws with a stochastically driven flux

Giovanni Russo Shock capturing schemes for all Mach number flow in gas dynamics

Lev Truskinovsky Solitary waves in the FPU lattice: from quasi-continuum to anti-continuum limit


Schedule of the workshop

Tuesday afternoon

2pm-2:45pm: C. Makridakis

2:45-3:30pm: C. Pares

3:30pm: coffee break

4pm-4:45pm G. Russo

Wednesday morning

10am-10:45am: S. Gavrilyuk

10:45am: coffee break

11:15am: C. Chalons

Noon: lunch buffet

Wednesday afternoon

2pm-2:45pm R. Abgrall

2:45pm-3:30pm S. Mishra

3:30am coffee break

4pm L. Truskinovsky

Thursday morning

9:30am-10:15am N. Risebro

10:15am coffee break

10:45am B. Boutin

11:30am P. Marcati

12:15 lunch buffet (end of the workshop)



Participants to the workshop


Other practical informations

The workshop will take place in the main lecture room 309 of the Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, which is located in the building 15-16.

Address: 4 Place Jussieu, 75258 Paris. Subway station: Jussieu.

List of hotels in the vicinity of the university

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Seminar at the

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie, Paris

Organizers

 Philippe G. LeFloch (Paris)

 Jacques Smulevici (Orsay)

Jérémie Szeftel (Paris)


 This Fall: October 10, November 21, and December 12, 2016


 

Monday October 10, 2016

room 15/25-104

 

 14h Peter Hintz (Berkeley)

Nonlinear stability of Kerr-de Sitter black holes

Abstract. In joint work with András Vasy, we recently established the stability of the Kerr-de Sitter family of black holes as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta but without any symmetry assumptions on the initial data. I will explain the general framework which enables us to deal systematically with the diffeomorphism invariance of Einstein’s equations, and thus how our solution scheme finds a suitable (wave map type) gauge within a carefully chosen finite-dimensional family of gauges; I will also address the issue of finding the mass and the angular momentum of the final black hole.

 15h30 Stefan Czimek (Paris)

An extension procedure for the constraint equations

Abstract. In this talk we present a new extension procedure for the maximal constraint equations of general relativity, motivated by applications to the Cauchy problem. Given a small solution on the unit ball, we can extend it to an asymptotically flat global solution. The main features are that our extension procedure does not need a gluing region, preserves regularity and works in weak regularity. For the proof, we use new methods to solve the prescribed divergence equation for the second fundamental form and the prescribed scalar curvature equation for the metric. We use the under-determinedness of the constraint equations to conserve regularity.

 


 

Monday November 21, 2016

room 15/16-413

 

14h The-Cang Nguyen (Paris)

Progress and recent results for the conformal equations

Abstract. The presentation will be divided into two parts. First, I will introduce the conformal equations and present recent results for these equations as well as questions arising naturally. In a second part, I will talk about the “half-continuity method” and explain how to use this method for giving answers to the questions posed in the first part.

15h30 Volker Schlue (Paris)

On the nonlinear stability of expanding black hole cosmologies

 


 

Monday December 12, 2016

room 15/25-102

 

14h Michał Wrochna (Grenoble)

The quantum stress-energy tensor and its intricate relationship with spacetime geometry

Abstract. It is widely believed that at low energies, quantum gravity should yield an effective theory described by Einstein equations with a stress-energy tensor made of averaged fluctuations of quantum fields. The construction of that stress-energy tensor is however very problematic and its intricate dependence on spacetime geometry results in highly non-linear equations that possess no qualitative theory to date. In this talk I will review this problem as a motivation for improving the construction of linear Klein-Gordon quantum fields, and discuss recent progress that allows for a better control of the dependence on the spacetime metric (partly based on joint work with Christian Gérard).

15h30 Guillaume Idelon-Riton (Regensburg)

Some results about the scattering theory for the massive Dirac fields in the Schwarzschild-Anti-de Sitter space-time

Abstract.  I will first give a brief presentation of the Schwarzschild-Anti-de Sitter spacetime and of some of its geometrical properties that will concern us. Then I will present the massive Dirac equation in this space-time and first study the Cauchy problem which is not completely obvious since our spacetime is not globally hyperbolic. I will then give a result concerning the asymptotic completeness for these fields. By means of a Mourre estimate, it is possible to obtain that the minimal velocity for these fields is 1. I will then show that our dynamics behaves in asymptotic regions like a transport at unit speed in the direction of the black hole. In a third part, I will study the local energy decay for these fields. First, using the existence of exponentially accurate quasi-modes, I will show a logarithmic lower bound on the local energy decay which is in accordance with the results of G. Holzegel and J. Smulevici in the Kerr-Anti-de Sitter spacetime for the Klein-Gordon fields. In order to obtain an upper bound, I will prove the existence of resonances and give some tools in order to localize them.

 

11th DFG–CNRS WORKSHOP Micro-Macro Modeling and Simulation of Liquid-Vapor Flows

organized with the financial support of

DFG, CNRS, and ITN

Wednesday March 2nd, 2016 (afternoon) 

to  Friday March 4th, 2016 (at noon)

Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4, Place Jussieu, Paris. Subway station: Jussieu 

Lecture room 15-16 — 309

____________________________

 
INVITED SPEAKERS
 
 

Nina Aguillon (Paris) 

Christophe Berthon (Nantes)

Christophe Chalons (Versailles) 

Frédéric Coquel (Palaiseau)

Johannes Daube (Freiburg)

Bruno Després (Paris)

Christian Dickopp (Aachen)

Florence Drui (Châtenay-Malabry) 

Robert Eymard  (Marne-La-Vallée)

Jan Giesselman (Stuttgart)

Philippe Helluy (Strasbourg)

Mirko Kraenkel (Freiburg)

Dietmar Kroener (Freiburg)

Rüdiger Müller (Berlin)

Carlos Pares (Malaga)

Arnold Reusken (Aachen)


 

____________________________

Main organizer

Philippe G. LeFloch (Paris)

Co-organizers

Dietmar Kroener (Freiburg)

Frédéric Coquel (Palaiseau)


SCHEDULE

 

Wednesday afternoon (Chairman P.G. LeFloch) 

 

14h30 -15h Robert Eymard  (Marne-La-Vallée)
15h – 15h30 Jan Giesselman (Stuttgart)
15h30 – 16h Coffee break
16h-16h30 Philippe Helluy (Strasbourg)
16h30-17h Mirko Kraenkel (Freiburg)

 

Thursday morning  (Chairman Jan Giesselman)

 

10h-10h30 Christophe Berthon (Nantes)
10h30-11h Johannes Daube (Freiburg)
11h-11h30 Coffee break 
11h30-12h Christophe Chalons (Versailles)
12h-12h30 Dietmar Kroener (Freiburg)
12h30-14h30 Lunch break

 

Thursday afternoon (Chairman F. Coquel) 

 

14h30-15h Bruno Després (Paris)
15h-15h30 Arnold Reusken (Aachen)
15h30-16h Coffee break
16h-16h30 Nina Aguillon (Paris)
16h30-17h Rüdiger Müller (Berlin)

 

Friday morning (Chairman D. Kroener)

 

10h-10h30 Carlos Pares (Malaga)
10h30-11h Florence Drui (Châtenay-Malabry)
11h-11h30 Coffee break
11h30-12h Christian Dickopp (Aachen)
12h-12h30 Frédéric Coquel (Palaiseau)

 


TITLES and ABSTRACTS 

 

Nina Aguillon (Paris)  Numerical approximation of hyperbolic systems containing an interface 
Abstract. We present an approach to approximate numerically the solution of coupled hyperbolic conservation laws. The coupling is achieved through a fixed interface, in which interface conditions are linking the traces on both sides. The main interest of the scheme is that it does not use the knowledge of the solution to the Riemann problem, and hence it is quite flexible and easy to implement. The idea of the scheme is to balance the effects ot the waves that enter the interface, in order to numerically mimic the structure of the Riemann problem. The scheme is well balanced with respect to all the piecewise equilibria associated with the interface conditions. If one of the interface condition is the conservation of a conserved variable, the scheme maintains it exactly. We will present a detailed analysis in the classical case, and a variety of test cases assessing the quality of the method. This is a joint work with Raul Borsche (Technische Universität Kaiserslautern)

Christophe Berthon (Nantes)  Numerical convergence rate for a diffusive limit of hyperbolic systems: p-system with damping

 

Christophe Chalons (Versailles)  On all regime Lagrangian-remap numerical schemes for compressible fluid systems
Abstract. It is the purpose of this contribution to provide an overview on recent advances in the development of all-regime Lagrange-Remap numerical schemes for compressible fluids systems with source terms. We will consider in particular the case of large friction coefficients and the case of low-Mach numbers. More precisely, we will present a discretization strategy for gas dynamics equations for unstructured grids based on a Lagrange-Remap approach that does not involve any moving mesh. A natural semi-implicit extension of the method that allows to remain stable under a CFL condition involving only the material velocity will be given, together with an extremely simple modification that allows to provide an accurate and stable solver for simulations involving low-Mach regions in the flow. The stability properties of the proposed schemes and several numerical experiments will be presented. This contribution is based on a series of joint works with Mathieu Girardin and Samuel Kokh. These works were performed during M. Girardin’s PhD thesis.

 

Johannes Daube (Freiburg)  Sharp interface limit for the Navier–Stokes–Korteweg model

Abstract. The Navier–Stokes–Korteweg model, an extension of the compressible Navier–Stokes equations, is a diffuse interface model for liquid-vapour flows which allows for phase transitions. In the model, a small parameter represents the thickness of an interfacial area, where phase transitions occur. Its static version was studied by Hermsdoerfer, Kraus and Kroener and the corresponding interface conditions were obtained. Assuming convergence of an associated energy functional to a suitable surface measure, we will perform the sharp interface limit in the dynamic case. More precisely, by means of compactness, we will ensure that solutions to the diffusive Navier-Stokes-Korteweg equations converge to solutions of an appropriate sharp interface model as the interface thickness tends to zero. This is joint work with H. Abels (Regensburg), C. Kraus (Wuerzburg-Schweinfurt) and D. Kroener (Freiburg).

 

Bruno Després (Paris) Modeling uncertainties with  kinetic equations
Abstract: The modeling of uncertainties is fundamental in industry and in CFD. For  nonlinear equations, it   questions the compatibility of L1-BV techniques (for conservation laws)  with L2 approaches (for the uncertainties). I will review recent progresses on the modeling at the kinetic level (with B. Perthame), and present recent ideas  which show connection of the so-called kinetic polynomials with optimal control (with E. Treat).

 

Christian Dickopp (Aachen) Coupling of (elastic)-plastic solids with compressible two-phase fllows for cavitation damaging
Abstract. As a model problem to investigate cavitation damaging the collapse of a single gas bubble collapsing near to an elastic or elastic-plastic solid wall is simulated numerically. This transient three-phase system is  modeled by the compressible Euler equations completed by a stiffened gas law for both fluids, where the liquid and the gas phase are distinguished  by a level set approach, and either the pure elastodynamical equations for a linear-elastic solid or an extension to describe plastic effects. A weak coupling strategy connects the alternating calculations of the fluid solver and  the solid solver using transient boundary conditions that are updated by the other solver.

 

Florence Drui (Châtenay-Malabry) A hierachy of homogeneous two-fluid models and numerical methods for simulating various regimes of two-phase flows
Abstract. Compressible two-fluid models offer a potential solution for simulating separated two-phase flows configurations. On the other hand, a specific family of such models has been developed for the regime of dispersed gas bubbles and show good agreement with experiments in the case of small acoustic perturbations. On the way to connect both types of flows, we propose here a hierarchy of homogeneous two-fluid models. Starting with Hamilton’s variational principle and adding thermodynamically consistent dissipative structures, we built a new connected hierarchy, each level of which being mathematically well-posed. Every new relaxation small parameter is physically identified through acoustic linearization and analysis of the systems dispersion relations. Furthermore, numerical methods based on finite volume schemes are developed so as to preserve the properties of the models at the continuous level and to asymptotically handle the transition from each subsystem to another. Finally, simulations of simple academic configurations are performed and show the expected properties of the first models of the hierarchy, the numerical methods and dynamically adaptive mesh techniques with the potential for massively parallel simulations.

 

Robert Eymard  (Marne-La-Vallée) Convection and total variation flow
Abstract. We consider a simplified model, related to the flow of a nonNewtonian fluid. This simplified model consists in a scalar nonlinear hyperbolic equation, regularized by the total variation flow operator (or 1-Laplace operator). We give an entropy weak formulation, for which we prove the uniqueness of the solution using the doubling variable technique. We provide an existence result using the convergence of a numerical scheme, a splitting scheme where the hyperbolic flow is treated with finite volumes and the total variation flow with finite elements. Finally, some numerical simulations in 1D and 2D are presented. This work is a joint work with F. Bouchut and D. Doyen.

 

Jan Giesselman (Stuttgart) A priori error analysis of DG approximations of two-phase flows

Abstract. In this talk we consider a one dimensional  model for isothermal two-phase flows using Lagrangian coordinates. The model is of diffuse interface type with a non-monotone pressure law. We will present a priori error analysis of a semi-discrete discontinuous Galerkin method, which satisfies a discrete version of the energy inequality which is valid on the continuous level. It also satisfies a relative energy type stability theory. Combining this stability framework with suitable projection operators for the exact solution allows us to derive optimal order error estimates. We will also present numerical results obtained using a fully-discrete version of the scheme, which validate our theoretical results.

 

Philippe Helluy (Strasbourg) Task-based parallelization of a transport discontinuous Galerkin solver and applications.
Abstract. We present an implicit discontinuous Galerkin solver for the transport equation. Due to the upwind nature of the numerical flux, the linear system in the implicit step is block triangular. The scheme is thus well adapted to a task-based implementation. We present such an implementation using the StarPU library and we  discuss applications to fluid dynamics.

 

Mirko Kraenkel (Freiburg) Discontinuous Galerkin schemes for the Navier-Stokes-Allen-Cahn system

 

Dietmar Kroener (Freiburg) Conservation laws on surfaces

 

Rüdiger Müller (Berlin)  The Lippmann equation for liquid metal electrodes
Abstract. The Lippmann equation is considered as universal relationship between interfacial tension, double layer charge, and cell potential. Recently we have derived a general thermodynamically consistent model for electrochemical interfaces, which shows a remarkable agreement to single crystal experimental data. In this talk, we apply the model to a curved liquid metal electrode in contact with an electrolyte. By matched asymptotic analysis we obtain the Lippmann equation whenever the Debye length is small compared to electrode curvature radius. The interfacial tension of the Lippmann equation is composed of the surface tension of our general model, and additional contributions arising from the adjacent space charge layers. Comparison with experimental data of several mercury-electrolyte interfaces confirms the theoretical results. This is a joint work with Wolfgang Dreyer, Clemens Guhlke, and Manuel Landstorfer.

 

Carlos Pares (Malaga) Nonconservative products and Shallow Water models: an overview
Abstract. Many hyperbolic nonlinear PDE systems that include source terms and nonconservative products arise in the simulation of geophysical flows by means of depth-averaged models.  In this talk, a review of the numerical techniques developed in last years by my group of research and collaborators to solve this type of systems will be presented together with a discussion of the main difficulties  and challenges in this field. Some applications to the simulation of real flows will be shown to illustrate this topic.

 

Arnold Reusken (Aachen) Space-time unfitted FEM for problems with moving discontinuities
Abstract. In this talk we will discuss unfitted finite element methods (or CutFEM) in  a space-time setting. The motivation for the development of these methods comes from two-phase incompressible flows. We explain how these techniques can be applied for the accurate discretization of a mass transport equation and a two-phase flow (Navier-)Stokes equation. The idea of the method, rigorous error bounds for certain problem classes and results of numerical experiments will be presented.

Partial LIST of Participants
Boris Andreianov       boris.andreianov at lmpt.univ-tours.fr
Robert Eymard            robert.eymard at univ-mlv.fr
Jan Giesselmann      jan.giesselmann@mathematik.uni-stuttgart.de
Philippe Helluy      helluy at math.u-strasbg.fr
Mirko Keaenkel                kraenkel at mathematik.uni-freiburg.de
Bruno Despres          despres at ann.jussieu.fr
Christophe Berthon   christophe.berthon at math.univ-nantes.fr
Philippe LeFloch      contact at philippelefloch.org
Ruediger Mueller       mueller at wias-berlin.de
Arnold Reusken            reusken at igpm.rwth-aachen.de
Carlos Parés       pares at anamat.cie.uma.es
Johannes Daube              hannes at mathematik.uni-freiburg.de
Chalons Christophe christophe.chalons@uvsq.fr
Nina Aguillon      aguillon at ljll.math.upmc.fr
Christian Dickopp      dickopp at web.de
Florence Drui           florence.drui at centralesupelec.fr
Emmanuel Audusse     eaudusse at yahoo.fr
Gautier Dakin                 gautier.dakin at gmail.com
Roland Duclous            roland.duclous at gmail.com
Mehdi Khalloufi                mehdi.khalloufi at mines-paristech.fr
Pierre-Arnaud Raviart      pa at raviart.com
Frederic Coquel      frederic.coquel at cmap.polytechnique.fr
Dietmar Kroener      dietmar at mathematik.uni-freiburg.de 

____________________________

PRACTICAL INFORMATIONS 

How to come to the Laboratoire Jacques-Louis Lions

Hotels near the University Pierre et Marie Curie

____________________________


EARLIER WORKSHOPS “Micro-Macro Modeling and Simulation of Liquid-Vapor Flows”

Tenth Workshop, Freiburg, February 2015

Ninth Workshop, Paris, February 2014

Eight Workshop, Berlin, February 2013

Seventh Workshop, Paris, February 2012

Sixth Workshop, Stuttgart, January 2011

Fifth Workshop, Strasbourg, April 2010

Fourth Workshop, Aachen, February 2009

Third Workshop, Strasbourg, January 2008

Second Workshop, Bordeaux, November 2007

Opening Workshop, Kirchzarten, November 2005

September 14, 2015 to December 18, 2015

Trimester Program at the

Centre Emile Borel

Financial support provided by Institut Henri Poincaré

and ANR Project “Mathematical General Relativity”

Organizers

Lars Andersson (Potsdam)

Sergiu Klainerman (Princeton) 

Philippe G. LeFloch (Paris) 


MAIN THEMES OF THE PROGRAM

Einstein’s field equation of general relativity is one of the most important geometric partial differential equations. Over the past decade, the mathematical research on Einstein equation has made spectacular progress on many fronts (Cauchy problem, cosmic censorship, asymptotic behavior). These developments have brought into focus the deep connections between the Einstein equation and other important geometric PDE’s, including the wave map equation, Yang-Mills equation, Yamabe problem, as well as Hamilton’s Ricci flow. The field is of growing interest for mathematicians and of intense current activity, as is illustrated by major recent breakthrough, concerning the uniqueness and stability of the Kerr black hole model, the formation of trapped surfaces, and the bounded L2 curvature problem. Specifically, the themes of mathematical interest that will be developed in the present Program and are currently most active include:

  • The initial value problem for Einstein equation and the causal geometry of spacetimes with low regularity, formation of trapped surfaces
  • Techniques of Lorentzian geometry: injectivity radius estimates, geometry of null cones; construction of parametrix
  • Geometry of black hole spacetimes: uniqueness theorems, censorship principles
  • Coupling of Einstein equation for self-gravitating matter models, weakly regular spacetimes, nonlinear stability of Minkowski space with matter

General schedule for the Trimester

SCIENTIFIC ACTIVITIES during the Trimester


WORKSHOPS AND CONFERENCES

 REGISTER HERE 

Sept. 14 to 18, 2015 Summer School – INTRODUCTION TO MATHEMATICAL GENERAL RELATIVITY

List of speakers

Greg Galloway (Miami)

Gerhard Huisken (Tuebingen)

Hans Ringstrom (Stockholm)


Sept. 23 to 25, 2015  Workshop – RECENT ADVANCES IN MATHEMATICAL GENERAL RELATIVITY

List of speakers

Spyros Alexakis (Toronto)

Piotr Chrusciel (Vienna)

Joao Costa (Lisbon)

Semyon Dyatlov (Cambridge, USA)

Stefan Hollands (Cardiff)

Alexandru Ionescu (Princeton)

Lionel Mason (Oxford)

Vincent Moncrief (Yale)

Jean-Philippe Nicolas (Brest)

Harvey Reall (Cambridge, UK)

Hans Ringstrom (Stockholm)

Mu-Tao Wang (New York)


Sept. 28 to Oct. 1, 2015  Workshop – GEOMETRIC ASPECTS OF MATHEMATICAL RELATIVITY (Hold in Montpellier and organized by Marc Herzlich and Erwann Delay)

List of speakers

Piotr Chrusciel (Vienna)

Michael Eichmair (Zürich)

Mu-Tao Wang (New York)


Oct. 26 to 29, 2015  Workshop – DYNAMICS OF SELF-GRAVITATING MATTER

List of speakers

Hakan Andreasson (Gothenburg)

Thierry Barbot (Avignon)

Robert Beig (Vienna)

David Fajman (Vienna)

Marc Mars (Salamanca)

David Maxwell (Fairbanks)

Todd Oliynyk (Monash)

Volker Schlue (Toronto)

Bernd Schmidt (Potsdam)

Jared Speck (Cambridge, USA)

Shadi Tahvildar-Zadeh (Rutgers)

Eric Woolgar (Alberta)


Nov. 16 to  20, 2015  International Conference – GENERAL RELATIVITY – A Celebration of the 100th Anniversary

List of speakers        Schedule and title

Jean-Pierre Bourguignon (Bures-sur-Yvette)

Demetrios Christodoulou (Zürich & Athens)

Mihalis Dafermos (Princeton)

Thibault Damour (Bures-sur-Yvette)

Georges Ellis (Cape Town)

Richard Hamilton (New York)

Gustav Holzegel (London)

Jonathan Luk (Cambridge, UK)

Roger Penrose (Oxford)

Richard Schoen (Stanford & Irvine)

Jacques Smulevici (Orsay) 

Jérémie Szeftel (Paris)

Robert Wald (Chicago)

Qian Wang (Oxford)


Dec. 14 to 16, 2015  International Conference-  RELATIVITY AND GEOMETRY – IN MEMORY OF A. LICHNEROWICZ  (Organized by Giuseppe Dito, Jean-Pierre Francoise, Paul Gauduchon, Richard Kerner, Yvette Kosmann-Schwarzbach et Daniel Sternheimer)

List of speakers

Olivier Biquard  (Paris 6)

Robert Bryant (Durham)

Pierre Cartier (Gif-Sur-Yvette) 

Thibault Damour (Gif-Sur-Yvette) 

Nathalie Deruelle (Paris 7)

Simon Donaldson  (Stony Brook & London) 

Michel Dubois-Violette  (Paris 11)

Charles Francès (Strasbourg)

Edward Frenkel  (Berkeley)

Christian Fronsdal (Los Angeles)

Simone Gutt  (Bruxelles)

James Isenberg  (Eugene)  

Sergiu Klainerman  (Princeton) 

Maxim Kontsevich  (Gif-Sur-Yvette) 

Alan Weinstein  (Berkeley)



Program coordinated by the Centre Emile Borel at IHP. Financial support provided by the Institut Henri Poincaré and the ANR Project “Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”.


 
_____________________________________________________________________________________________________________

Organizers

Michael Anderson (Stony Brook)

Sergiu Klainerman (Princeton)

 Philippe G. LeFloch (Paris)

Jared Speck (Cambridge, USA)


Location: Simons Center for Geometry and Physics

Date: One-month concentration period in January 2015

Workshop from January 20 to 23, 2015


Einstein’s field equation of general relativity is one of the most important geometric partial differential equations. Over the past decade, the mathematical research on Einstein equation has made spectacular progress on many fronts, including the Cauchy problem, cosmic censorship, and asymptotic behavior. These developments have brought into focus the deep connections between the Einstein equation and other important geometric partial differential equations, including the wave map equation, Yang-Mills equation, Yamabe equation, as well as Hamilton’s Ricci flow. The field is of growing interest for mathematicians and of intense current activity, as is illustrated by major recent breakthroughs concerning the uniqueness and stability of black hole models, the formation of trapped surfaces, and the bounded L2 curvature problem. The themes of mathematical interest that will be particularly developed in the present Program include the formation of trapped surfaces and the nonlinear interaction of gravitational waves. The new results are based on a vast extension of the earlier technique by Christodoulou and Klainerman establishing the nonlinear stability of the Minkowski space. This Program will be an excellent place in order to present the recent breakthrough on the bounded L2 curvature problem for the Einstein equation, which currently provides the lower regularity theory for the initial value problem, as well as the recently developed theory of weakly regular Einstein spacetimes with distributional curvature.

Long-term participants

Michael Anderson (Stony Brook)

Piotr Chrusciel (Vienna)

Mihalis Dafermos (Princeton)

Cécile Huneau (Paris)

Alexandru D. Ionescu (Princeton)

James Isenberg (Eugene)

Sergiu Klainerman (Princeton)

Philippe G. LeFloch (Paris)

Jared Speck (Cambridge, USA)

Jinhua Wang (Hangzhou)

Mu-Tao Wang (New York)

Qian Wang (Oxford)

Willie Wong (Lausanne)

Speakers during the Workshop

  • Tuesday January 20
    • Sung-Ji Oh (Berkeley) Linear instability of the Cauchy horizon in subextremal Reissner-Nordström spacetime under scalar perturbations
    • Volker Schlue (Toronto) Stationarity of time-periodic vacuum spacetimes
    • Alexandru D. Ionescu (Princeton) The Euler–Maxwell system for electrons: global solutions in 2D
    • Joachim Krieger (Lausanne) Concentration-compactness for the critical Maxwell-Klein-Gordon equation
  • Wednesday January 21
    • Xianliang An (Piscataway) Two results on formation of trapped surfaces
    • Tahvildar-Zadeh (Piscataway) The Dirac electron and the Kerr-Newman spacetime
    • Mihalis Dafermos (Princeton)
    • Jim Isenberg (Eugene) Asymptotically hyperbolic shear-free solutions of the Einstein constraint equations
  • Thursday January 22
    • Cécile Huneau (Paris) Stability in exponential time of Minkowski
    • Jacques Smulevici (Orsay) Vector field methods for transport equations with applications to the Vlasov-Poisson system
    • Mu-Tao Wang (New York) Quasi-local angular momentum and the limit at infinity
    • Spyros Alexakis (Toronto) The Penrose inequality for perturbations of the Schwarzschild exterior
  • Friday January 23
    • Mihai Tohaneanu (Statesboro) Pointwise decay for the Maxwell system on black holes
    • Qian Wang (Oxford)
    • Peter Blue (Edinburgh) Revisiting decay of fields outside a Schwarzschild black hole
    • Philippe G. LeFloch (Paris) Weak solutions to the Einstein equations in spherical or T2 symmetry

Attendees List

Philippe LeFloch, DIRECTOR OF RESEARCH AT CNRS contact@philippelefloch.org philippelefloch.org

IHP PROGRAM

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