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

TL;DR

This paper establishes a priori estimates for the linearized relativistic Euler equations with a physical vacuum boundary, focusing on thermodynamic variables and energy estimates in weighted Sobolev spaces.

Contribution

It introduces a novel approach to deriving energy estimates for the linearized system with a physical vacuum boundary in the relativistic Euler equations.

Findings

Proved a priori estimates in weighted Sobolev spaces.

Developed a weighted book-keeping scheme for thermodynamic variables.

Established energy estimates for the linearized relativistic Euler system.

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.