Remarks on the Einstein-Euler-Entropy system

Abstract

We prove short-time existence for the Einstein-Euler-Entropy system for non-isentropic fluids with data in uniformly local Sobolev spaces. The cases of compact as well as non-compact Cauchy surfaces are covered. The method employed uses a Lagrangian description of the fluid flow which is based on techniques developed by Friedrich, hence providing a completely different proof of earlier results of Choquet-Bruhat and Lichnerowicz. This new proof is specially suited for applications to self-gravitating fluid bodies.

References in corpus (2)

• On the limit of large surface tension for a fluid motion with free boundary
• On the Choquet-Bruhat-York-Friedrich formulation of the Einstein-Euler equations

Cited by in corpus (6)

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• Nonlinear causality of general first-order relativistic viscous hydrodynamics
• Causality of the Einstein-Israel-Stewart Theory with Bulk Viscosity
• The relativistic Euler equations with a physical vacuum boundary: Hadamard local well-posedness, rough solutions, and continuation criterion
• On the well-posedness of relativistic viscous fluids with non-zero vorticity
• Breakdown of smooth solutions to the Müller-Israel-Stewart equations of relativistic viscous fluids