A priori estimates for the linearized relativistic Euler equations with a physical vacuum boundary and an ideal gas equation of state

2024/11/20 by Brian B. Luczak, Luczak, Brian B.
Mathematics · #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2411.13726

Abstract

In this paper, we will provide a result on the relativistic Euler equations for an ideal gas equation of state and a physical vacuum boundary. More specifically, we will prove a priori estimates for the linearized system in weighted Sobolev spaces. Our focus will be on choosing the correct thermodynamic variables, developing a weighted book-keeping scheme, and then proving energy estimates for the linearized system.

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