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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.
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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
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
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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
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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 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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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 Nov. 24, 2011
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris
Lecture room 15-25 326 (third floor)
14h Paul Laurain (Paris 7) Surfaces with constant mean curvature in a Riemannian manifold of dimension 3
Abstract. The surfaces with constant mean curvature (CMC) in a spacelike hypersurface are geometrically and physically very interesting, as shown by Huisken and Yau in 1996 or in the beautiful thesis of Bray. However, the purpose of this talk is not to develop the physical properties of CMC surfaces but to see on an example what are the analytical difficulties encountered when studying these surfaces. In fact, we will show how to study CMC surfaces in terms of partial differential equations in order to derive geometric properties. We emphasize in particular the key difficulties generated by the conformal invariance of the problem as the phenomena of concentration and we will show how the structure of the equation helps us to overcome them.
15h30 James D.E. Grant (Vienna) Null injectivity radius estimates
Abstract. I will report on joint work with P.G. LeFloch, in which we use comparison techniques, such as the Rauch comparison theorem and Hessian comparison theorem, to estimate the null injectivity radius on a Lorentzian manifold. This work gives a more geometrical setting for work of Klainerman and Rodnianski on null injectivity radius estimates.
