Nonlinear Stability of First-Order Relativistic Viscous Hydrodynamics

TL;DR

This paper establishes the nonlinear stability of homogeneous states in second-order hyperbolic models of dissipative relativistic fluids, using a dissipativity criterion and recent stability results for small-data solutions.

Contribution

It introduces a novel stability analysis for second-order hyperbolic relativistic fluid models, extending previous theoretical frameworks.

Findings

Proves nonlinear stability of homogeneous states

Validates dissipativity criterion for these systems

Ensures long-time existence and stability of solutions

Abstract

This paper shows nonlinear stability of homogeneous states in second-order hyperbolic systems of partial differential equations that model the dynamics of dissipative relativistic fluids, by checking a dissipativity criterion formulated earlier by the authors and invoking a recent general result by the second author on long-time existence and time-asymptotic stability of small-data solutions to nonlinear hyperbolic systems. Version 3 differs from version 2 by a trivial correction (minus signs in front of six coefficients).