Local well-posedness in Sobolev spaces for first-order barotropic causal relativistic viscous hydrodynamics

TL;DR

This paper proves local well-posedness of a causal, stable first-order relativistic viscous hydrodynamics theory in Sobolev spaces, improving previous results that were limited to Gevrey spaces.

Contribution

It establishes local well-posedness in Sobolev spaces for a first-order relativistic viscous hydrodynamics model, enhancing the mathematical understanding of the theory.

Findings

Proved local well-posedness in Sobolev spaces.

Improved mathematical framework for relativistic viscous fluids.

Enhanced stability and causality analysis.

Abstract

We study the theory of relativistic viscous hydrodynamics introduced in arXiv:1109.0985 and arXiv:1907.12695, which provided a causal and stable first-order theory of relativistic fluids with viscosity in the case of barotropic fluids. The local well-posedness of its equations of motion has been previously established in Gevrey spaces. Here, we improve this result by proving local well-posedness in Sobolev spaces.