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A symmetrization of the relativistic Euler equations in several spatial variables

Authors
  • LeFloch, Philippe G.
  • Ukai, Seiji
Type
Preprint
Publication Date
Dec 20, 2008
Submission Date
Dec 20, 2008
Source
arXiv
License
Yellow
External links

Abstract

We consider the Euler equations governing relativistic compressible fluids evolving in the Minkowski spacetime with several spatial variables. We propose a new symmetrization which makes sense for solutions containing vacuum states and, for instance, applies to the case of compactly supported solutions, which are important to model star dynamics. Then, relying on these symmetrization and assuming that the velocity does not exceed some threshold and remains bounded away from the light speed, we deduce a local-in-time existence result for solutions containing vacuum states. We also observe that the support of compactly supported solutions does not expand as time evolves.

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