A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary
Name
1511.07467.pdf
Description
Submitted version
Size
518.56 KB
Format
Adobe PDF
Checksum (MD5)
5d27d2827adfae7d2661cf069def6ca6
Author(s)
Speck, Jared R.
Date Issued
October 2019
Journal
Communications in partial differential equations
Publisher
Taylor & Francis Group, LLC.
Citation
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)
Version
Original manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1080/03605302.2019.1583250
