Generic stability of dissipative non-relativistic and relativistic fluids

TL;DR

This paper proves the asymptotic stability of homogeneous equilibrium in both non-relativistic and relativistic dissipative fluids, based solely on thermodynamic stability and nonnegative transport coefficients.

Contribution

It establishes a general stability proof for dissipative fluids in both non-relativistic and relativistic regimes using thermodynamic restrictions.

Findings

Equilibrium is asymptotically stable in both fluid types.

Stability depends only on thermodynamic stability and nonnegative transport coefficients.

The proof applies to fluids with mass flux and relativistic energy vector internal energy.

Abstract

The linear stability of the homogeneous equilibrium of non-relativistic fluids with mass flux and special relativistic fluids with the absolute value of the energy vector as internal energy is investigated. It is proved that the equilibrium is asymptotically stable in both cases due to purely thermodynamic restrictions; the only requirements are the thermodynamic stability and the nonnegativity of the transport coefficients.