The stability of one dimensional stationary flows of compressible viscous fluids

Abstract

In [1], § 5 we gave a necessary and sufficient condition for the existence of stationary solutions for the system (1.1) in the presence of arbitrarily large external forces $f(x)$. Here we prove, see theorem 2.1, that every stationary solution is necessarily stable. We use Euler coordinates, since a proof in Lagrange coordinates (see for instance [2], [3], [4]) should present greater obstacles.

Résumé

On démontre que toute solution du système d’équations décrivant le mouvement unidimensionnel d’un fluide compressible et visqueux (avec des forces arbitraires et indépendantes du temps) est nécessairement stable.