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

Brian B. Luczak

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arXiv · 2411.13726

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

Brian B. Luczak

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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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Brian B. Luczak. 2024-11-20. A priori estimates for the linearized relativistic Euler equations with a physical vacuum boundary and an ideal gas equation of state. https://arxiv.org/abs/2411.13726

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