Seminar on Mathematical General Relativity — March 22, 2012

March 2, 2012 in ALL SEMINARS AND CONFERENCES, GENERAL RELATIVITY | Tags: | Leave a comment

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Seminar on

Mathematical General Relativity

Organizers:

 Philippe G. LeFloch (Univ. Pierre et Marie Curie)

Ghani Zeghib (Ecole Normale Supérieure, Lyon)

ANR Project

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


Thursday March 22, 2012

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

Lecture room 15-25 102 (first level)


14h   Mihalis Dafermos (Cambridge) Black holes without spacelike singularities

Abstract.   It is shown that for small, spherically symmetric perturbations of asymptotically flat two-ended Reissner-Nordstroom data for the Einstein-Maxwell-real scalar field system, the boundary of the dynamic spacetime which evolves is globally represented by a bifurcate null hypersurface across which the metric extends continuously. Under additional assumptions, it is shown that the Hawking mass blows up identically along this bifurcate null hypersurface, and thus the metric cannot be extended twice differentiably, in fact, cannot be extended in a weaker sense characterized at the level of the Christoffel symbols. The proof combines estimates obtained in previous work with an elementary Cauchy stability argument. There are no restrictions on the size of the support of the scalar field, and the result applies to both the future and past boundary of spacetime. In particular, it follows that for an open set in the moduli space of solutions around Reissner-Nordstrom, there is no spacelike component of either the future or the past singularity.

15h30  Rabah Souam (Paris)  Harmonic diffeomorphisms and maximal surfaces

Abstract.  We study the existence (or the non-existence) of harmonic diffeomorphisms between certain domains in the Euclidean  two-sphere. In particular, we construct harmonic diffeomorphisms from circular domains in the complex plane onto finitely punctured spheres, with at least two punctures. This result follows from a general existence theorem for maximal graphs with isolated singularities in the Lorentzian product M x R, where M is an arbitrary n-dimensional compact Riemannian manifold (with n larger than 1).  In contrast, we show that there is no harmonic diffeomorphism from the unit complex disc onto the (once) punctured sphere, and no harmonic diffeomeorphisms from finitely punctured spheres onto circular domains in the Euclidean two-sphere. This is a joint work with Antonio Alarcon.

Seminar on Mathematical General Relativity_____ February 9, 2012

January 7, 2012 in ALL SEMINARS AND CONFERENCES, GENERAL RELATIVITY | Tags: | Leave a comment

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Seminar on

Mathematical General Relativity

Organizers:

 Philippe G. LeFloch (Univ. Pierre et Marie Curie)

Ghani Zeghib (Ecole Normale Supérieure, Lyon)

With the financial support of the ANR Project

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


Thursday February 9, 2012

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

Lecture room 15-25 101 (first level)


14h   Alan Rendall (AEI, Potsdam) Singularity formation in solutions of the Einstein-Vlasov system

Abstract.  Important questions in mathematical relativity are when singularities form in solutions of the Einstein equations coupled to matter and, in cases where they do form, what their qualitative nature is. A type of matter model which apparently rarely loses smoothness in the absence of black hole formation is collisionless matter modelled by the Vlasov equation. This contrasts with dust, a type of matter popular among relativists. In this talk I describe recent work with Juan Velazquez where we try to obtain new insights about the dynamics of the Einstein-Vlasov system by interpolating between smooth Vlasov and dust in a suitable way. We have shown that for certain mildly singular initial data a curvature singularity can form. It is constructed by means of a shooting argument for a system of ordinary differential equations. From the point of view of physics it would be desirable to improve this solution in various ways and I will report briefly on work in progress on doing this.

15h30 François Filastre (Cergy-Pontoise) Brunn–Minkowski theory in Minkowski spacetime 

Abstract.  The Brunn–Minkowski theory deals with the relations between the addition and the volume of convex bodies of the Euclidean space. Convex bodies are described by function on the sphere. The main result of the theory is that the volume is log-concave. We establish an analog result for a class of convex sets in the Minkowski spacetime. The compactness is replaced by a global invariance property under the action of particular groups of linear isometries. In particular, these convex sets can be described by functions on compact hyperbolic manifolds and, in this case, the volume is convex.

Workshop Two-Phase Fluid Flows – Feb. 14 to 16, 2012

December 8, 2011 in ALL SEMINARS AND CONFERENCES, COMPRESSIBLE FLUIDS | Tags: , | Comments closed

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7th DFG–CNRS WORKSHOP

Two-Phase Fluid Flows. Modeling and Computational Methods 

Main organizer:    

 Philippe G. LeFloch (Univ. Pierre et Marie Curie, Paris)

Co-organizers:

Christophe Berthon (Nantes) and Philippe Helluy (Strasbourg)

With financial support from the DFG and the CNRS


Tuesday Feb. 14, 2012 at 2pm to Thursday Feb. 16 at noon

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

Subway station: Jussieu

Lecture room 15-16 — 309


SCHEDULE, list of participants, and abstracts


INVITED SPEAKERS


Gonca Aki (Berlin) An incompressible diffuse flow with phase transition

Mathieu Bachmann (Aachen) Numerical simulation of shock wave-bubble interactions using laser-induced cavitation bubbles

Frank Boyer (Marseille)  Numerical methods for a three-component phase field model

Sergey L. Gavrilyuck (Marseille) Diffuse interface model for compressible fluid-compressible elastic-plastic solid interaction

Maren Hantke (Magdeburg) Exact solutions to the Riemann problem for compressible isothermal Euler equations for two phase flows, with and without phase transition

Jonathan Jung (Strasbourg) Computing bubble oscillations on GPU (graphics processing unit)

Mirco Kraenkel (Freiburg) Numerics for phase field models

Hélène Mathis (Nantes) Model adaptation for hyperbolic systems with relaxation 

Khaled Saleh (Paris) A splitting method for the isentropic Baer-Nunziato two-phase flow model 

Nicolas Seguin (Paris)  Model adaptation in hierarchies of hyperbolic systems

Gabriele Witterstein (Munich) Existence of transition profiles for compressible flows

Christophe Zeiler (Stuttgart) Curvature driven liquid-vapor flow of compressible fluids

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PRACTICAL INFORMATIONS 

LIST OF PARTICIPANTS

How to come to the Laboratoire Jacques-Louis Lions ?

Hotels near the University Pierre et Marie Curie ?

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

Sixth Workshop, Stuttgart, Jan. 2011

Fourth Workshop, Aachen, Feb. 2009

Second Workshop, Bordeaux

Opening Workshop, Kirchzarten, Nov. 2005

Seminar on Compressible Fluids – January 10, 2012

December 7, 2011 in ALL SEMINARS AND CONFERENCES, COMPRESSIBLE FLUIDS | Tags: | Comments closed

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Seminar on Compressible Fluids

Tuesday January 10, 2012

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie

4 Place Jussieu, 75258  Paris

Building 15/16. Lecture room 309

With the support of LRC MANON

  • 14h00 : Philippe Helluy (Strasbourg) Résolution des équations de Maxwell-Vlasov sur GPU

Abstract.  Je présenterai un couplage d’une méthode Galerkin-Discontinu et d’une méthode PIC (Particle-In-Cell) pour la résolution des équations de Vlasov-Maxwell. Ces méthodes ont déjà été implémentées à de nombreuses reprises. La nouveauté consiste ici à le faire sur une carte graphique avec le langage OpenCL, ce qui conduit à des façons différentes d’organiser l’algorithme de couplage.

  • 15h30 : Christophe Berthon (Nantes)  Schémas hydrostatiques décentrés pour les équations shallow-water

Abstract.  We consider the numerical approximation of the shallow–water equations with non–flat topography. We introduce a new topographic discretization which makes all schemes to be well–balanced and robust. In contrast with the well–known hydrostatic reconstruction, the proposed numerical procedure does not involve any cut–off. Moreover, the proposed scheme is able to deal with dry areas. Several numerical benchmarks are presented to assert the interest of the method.

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Organizers: Frédéric Coquel, Edwige Godlewski, et Philippe LeFloch

Seminar on Mathematical General Relativity_____ January 5, 2012

December 2, 2011 in ALL SEMINARS AND CONFERENCES, GENERAL RELATIVITY | Tags: | Comments closed

___________________________________________________________________________________________________________________________________________

Seminar on

Mathematical General Relativity

Organizers:

 Philippe G. LeFloch (Univ. Pierre et Marie Curie)

Ghani Zeghib (Ecole Normale Supérieure, Lyon)

With the financial support of the ANR Project

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


Thursday January 5, 2012

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

Lecture room 15-25 326 (third floor)


14h  Alain Bachelot (Bordeaux) Klein-Gordon equation on the Anti-de Sitter universe AdS5

Abstract.  We consider the Klein-Gordon equation on the Poincaré chart of the 5-dimensional Anti-de Sitter universe. When the mass is larger than −1, the Cauchy problem is well posed despite the loss of global hyperbolicity due to the time-like horizon. We express all finite energy solutions in the form of a continuous Kaluza-Klein tower. We investigate the case of gravitational fluctuations, and  electromagnetic waves. The propagation of the wave front set shows that the horizon acts like a perfect mirror. We establish several results on the asymptotic behavior: dispersive estimates, global Strichartz estimates, existence of a lacuna, equi-partition of the energy. We address the cosmological model of the `negative tension’ Minkowski brane. We prove that the hyperbolic mixed problem is well-posed and that all normalizable solutions can be expanded in a discrete Kaluza-Klein tower. Finally, we obtain some L2−L∞ estimates in suitable weighted Sobolev spaces.

15h30 Gilles Carron (Nantes) Rigidity of critical metrics

Abstract. We explain how an elementary idea (existence of bubble of curvature) can be used to proved new and old rigidity results for critical metrics. For instance, we re-prove an old result by M. Anderson that, for an Einstein metric, we get a control on the curvature from a control on the volume.

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Philippe LeFloch -- CNRS DIRECTOR OF RESEARCH -- Email: contact at philippelefloch dot org

IHP PROGRAM 2015

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