Hyperbolic conservation laws and spacetimes with limited regularity

Details Hyperbolic conservation laws and spacetimes with limited regularity Hyperbolic conservation laws and spacetimes with limited regularity

2007-11-02

arxiv.org/abs/0711.0403v1

Mathematics

Analysis of PDEs

11 pages, Proceedings

Scientific paper

Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows and general relativity. Recent work by the author and his collaborators attempts to set the foundations for a study of weak solutions defined on Riemannian or Lorentzian manifolds and includes an investigation of the existence and qualitative behavior of solutions. The metric on the manifold may either be fixed (shallow water equations on the sphere, for instance) or be one of the unknowns of the theory (Einstein-Euler equations of general relativity).

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