Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 10, pp. 1-60.

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

Author: Brian B. Luczak (Univ. of Chicago Laboratory Schools, Chicago, IL, USA)
  
Abstract:
In this article, 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.


Submitted November 27, 2024. Published January 27, 2025.
Math Subject Classifications: 35Q75, 35Q35, 35Q31, 35R37.
Key Words: Relativistic Euler equations; physical vacuum boundary; ideal gas equation of state.