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|a Speck, Jared R.
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|a Massachusetts Institute of Technology. Department of Mathematics
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|a A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary
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|b Taylor & Francis Group, LLC.,
|c 2020-08-19T12:01:07Z.
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|z Get fulltext
|u https://hdl.handle.net/1721.1/126672
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|a 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.
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|a National Science Foundation (U.S.) (Grant DMS-1162211)
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|a National Science Foundation (U.S.) (Career Grant 454419)
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|a en
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|a Article
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|t 10.1080/03605302.2019.1583250
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|t Communications in partial differential equations
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