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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

and a project PICS CNRS


 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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Organizers

 Philippe G. LeFloch (Paris)

Jérémie Szeftel (Paris)

Ghani Zeghib (Lyon)

ANR Project

“Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”

Wednesday June 17, 2015

Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

Lecture room 15/25-326

 

11h Emmanuel Hebey (Cergy-Pontoise) Systèmes de Kirchhoff critiques stationnaires sur des variétés compactes

14h  Lydia Bieri (Ann Arbor) Gravitational radiation and two types of memory

Abstract.  We are believed to live on the verge of detection of gravitational waves, which are predicted by General Relativity. In order to understand gravitational radiation, we have to investigate analytic and geometric properties of corresponding solutions to the Einstein equations. Gravitational waves leave a footprint in the spacetime regions they pass, changing the manifold – and therefore displacing test masses – permanently. This is known as the memory effect. It has been believed that for the Einstein equations, being nonlinear, there exists one such effect with a small `linear’ and a large `nonlinear’ part. In this talk, I present some of my joint work with D. Garfinkle showing that these are in fact two different effects.

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Organizers

 Philippe G. LeFloch (Paris)

Jérémie Szeftel (Paris)

Ghani Zeghib (Lyon)

ANR Project

“Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”

Wednesday May 27, 2015

Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

Lecture room 15-25–326

 

14h Thierry Barbot (Avignon) Surfaces polygonales fuchsiennes et espace de Teichmüller décoré

Abstract. Dans l’article “Fuchsian polyhedra in Lorentzian space-forms, Mathematische Annalen 350, 2, pp. 417-453, 2011″, F. Fillastre a montré que toute métrique euclidienne avec singularités coniques d’angles > 2 pi sur une surface compacte se réalise de manière unique comme une surface de Cauchy polygonale dans un espace-temps globalement hyperbolique localement plat radial (i.e. dont le groupe d’holonomie fixe un point de l’espace de Minkowski). Dans cet exposé, j’évoquerai le travail de L. Brunswic dans son travail de thèse sous ma direction, qui vise à reprouver ce résultat et à l’étendre au cas des surfaces polygonales dans un espace-temps localement plat mais admettant des particules massives. Le but est de montrer qu’il y a encore existence et unicité une fois prescrit la masse des particules massives (le cas régulier montré par Fillastre correspondant au cas où l’angle singulier des particules massives est 2pi). Je montrerai aussi que la situation étudiée par R. Penner dans l’article “The Decorated Teichmϋller Space of Punctured Surfaces, Commun. Math. Phys. 113, 299-339 (1987)” est un cas limite de la situation étudiée par Brunswic, et correspond au cas où les particules sont d’angle conique nul. Je montrerai aussi comment répondre positivement à la question dans le cas où il n’y a qu’une singularité.

15h30 Andrea Seppi (Pavia) Convex surfaces in (2+1)-dimensional Minkowski space

Abstract.  It is known that the hyperbolic plane admits an isometric embedding into Minkowski space; in 1983 Hanu and Nomizu first observed the existence of non-equivalent isometric embeddings, thus showing a relevant difference with the Euclidean case. In this talk, I will introduce some natural properties of a convex surface in Minkowski space, concerning causality and asymptotic behavior. I will then explain some new results (jointly with Francesco Bonsante) on the classification of constant curvature surfaces with bounded principal curvatures and on the solvability of Minkowski problem in (2+1)-dimensional Minkowski space. If time permits, I will give the main ideas of the proof and especially the relation to some type of Monge-Ampere equations.

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Organizers

 Philippe G. LeFloch (Paris)

Jérémie Szeftel (Paris)

Ghani Zeghib (Lyon)

ANR Project

“Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”

Wednesday April 15, 2015

Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

Lecture room 15-25–326

 

14h Shiwu Yang (Cambridge) Decay properties of solutions of Maxwell Klein-Gordon equations

Abstract.  I will present some recent progress on the asymptotic behavior of global solutions to Maxwell-Klein-Gordon equations. I will show that the integrated local energy and the energy flux through the outgoing null hypersurfaces decays polynomially in the retarded time in Minkowski space with data merely bounded in some gauge invariant weighted Sobolev space. This in particular includes the case with large charge. One novelty of this work is that these decay estimates precisely capture the asymptotic properties for the non-linear fields with arbitrarily large data. If in addition that the initial data for the scalar field is sufficiently small, then we show the pointwise decay of the solutions. This result improves the previous result of Lindblad and Sterbenz in which smallness is required for both the scalar field and the Maxwell field.

15h30 Gustav Holzegel (London) Local and global dynamics in asymptotically anti de Sitter spacetimes

Abstract.  Asymptotically anti de Sitter (aAdS) spacetimes play a prominent role in theoretical physics and mathematics.  Due to the presence of a timelike hypersurface at infinity these spacetimes are not globally hyperbolic, a fact that leads to intricate initial boundary value problems when studying global dynamics of hyperbolic equations on these backgrounds. In this talk, I will present several local and global results for the massive wave equation on aAdS spacetimes (including black hole spacetimes) with emphasis on how different boundary conditions (Dirichlet, Neumann or dissipative) influence the global dynamics. In particular, I will outline a recent proof (obtained in collaboration with J. Luk, J. Smulevici and C. Warnick) of linear stability and decay for gravitational perturbations on anti de Sitter space under dissipative boundary conditions. The proof unravels an interesting trapping phenomenon near the conformal boundary which necessarily leads to a degeneration in the decay estimates. Time permitting some future applications will also be discussed.

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Organizers

 Philippe G. LeFloch (Paris)

Jérémie Szeftel (Paris)

Ghani Zeghib (Lyon)

ANR Project

“Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”

Wednesday March 4, 2015

Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

Lecture room 15-25–326

 

14h François Fillastre (Cergy-Pontoise) Minkowski problem in Minkowski space

Abstract. T. Barbot, F. Beguin and A. Zeghib solved a smooth Lorentzian version of the Minkowski problem in dimension (2+1). More precisely they proved that if M is a flat 3-dimensional maximal globally hyperbolic spatially compact spacetime, then there exists a unique strictly convex smooth space-like surface in M with a prescribed smooth positive Gauss curvature. We will look at this problem for any dimensions. The existence part is solved in a generalized way (a measure is prescribed rather than a function). Concerning the regularity of the solution, the 2+1 case is specific. The arguments are based on tools from the geometry of convex sets. Joint work with Francesco Bonsante (Pisa).

Philippe LeFloch, DIRECTOR OF RESEARCH AT CNRS Email address: pglefloch [at] gmail.com

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