A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary
Author(s)Speck, Jared R.
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Communications in partial differential equations
Taylor & Francis Group, LLC.
Hadžić, Mahir, Steve Shkoller and Jarad Speck. “A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary.” Communications in partial differential equations, vol. 44, no. 10, 2019, pp. 859-906 © 2019 The Author(s)