A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary
| Autor: | Jared Speck, Steve Shkoller, Mahir Hadžić |
|---|---|
| Přispěvatelé: | Massachusetts Institute of Technology. Department of Mathematics |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
35L70
35L80 83A05 76N10 Equation of state (cosmology) Astrophysics::High Energy Astrophysical Phenomena Applied Mathematics Nuclear Theory 010102 general mathematics FOS: Physical sciences Boundary (topology) Mathematical Physics (math-ph) Relativistic Euler equations 01 natural sciences 010101 applied mathematics General Relativity and Quantum Cosmology Mathematics - Analysis of PDEs Minkowski space FOS: Mathematics A priori and a posteriori 0101 mathematics Mathematical Physics Analysis Analysis of PDEs (math.AP) Mathematical physics Mathematics |
| Zdroj: | arXiv |
| Popis: | We study the relativistic Euler equations on the Minkowski spacetime background. We make assumptions on the equation of state and the initial data that are relativistic analogs of the well-known physical vacuum boundary condition, which has played an important role in prior work on the non-relativistic compressible Euler equations. Our main result is the derivation, relative to Lagrangian (also known as co-moving) coordinates, of local-in-time a priori estimates for the solution. The solution features a fluid-vacuum boundary, transported by the fluid four-velocity, along which the hyperbolicity of the equations degenerates. In this context, the relativistic Euler equations are equivalent to a degenerate quasilinear hyperbolic wave-map-like system that cannot be treated using standard energy methods. National Science Foundation (U.S.) (Grant DMS-1162211) National Science Foundation (U.S.) (Career Grant 454419) |
| Databáze: | OpenAIRE |
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