Displaying similar documents to “An introduction to the Einstein-Vlasov system”

Einstein-Euler equations for matter spacetimes with Gowdy symmetry

Philippe G. LeFloch (2008-2009)

Séminaire Équations aux dérivées partielles

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We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on T 3 . Given an arbitrary initial data set, we establish the existence of a globally hyperbolic future development and we provide a global foliation of this spacetime in terms of a geometrically defined time-function coinciding with the area of the orbits of the symmetry group. This allows us to construct matter spacetimes with weak regularity which admit,...

Blow-up for solutions of hyperbolic PDE and spacetime singularities

Alan D. Rendall (2000)

Journées équations aux dérivées partielles

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An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime singularities is naturally related to blow-up phenomena for nonlinear hyperbolic systems. These connections are explained and recent progress in applying the theory of hyperbolic equations in this field is presented. A direction which has turned out to be fruitful...

Regularity and geometric properties of solutions of the Einstein-Vacuum equations

Sergiu Klainerman, Igor Rodnianski (2002)

Journées équations aux dérivées partielles

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We review recent results concerning the study of rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. We develop new analytic methods based on Strichartz type inequalities which results in a gain of half a derivative relative to the classical result. Our methods blend paradifferential techniques with a geometric approach to the derivation of decay estimates. The latter allows us to take full advantage of the specific structure...