Existence of Viscous Profiles for the Compressible Navier—Stokes Equations

Abstract

In this article we show the existence of some particular solutions of the compressible Navier-Stokes equations called viscous profiles. The existence of such solutions provides an entropy criterion. The crucial point in the demonstration is the use of the center manifold theorem, and the main difficulty comes from the non-invertibility of the viscosity matrix in the Navier—Stokes equations.

Keywords:

• Viscous profiles
• Center manifold theorem
• Entropy condition
• Navier—Stokes equations

AMS Subject Classifications:

• 35L65 (35B35)