On the weak compactness of solutions to the equations of compressible flow

Abstract

The subject-matter of this paper is the study of weak limits (in appropriate function spaces) of solutions of equations describing nonstationary viscous compressible flows. We show that the classical entropy and energy estimates for solutions give enough information for proving that a weak limit of solutions is a distribution solution, provided we make certain additional assumptions on the boundedness of the density, velocity and temperature and an assumption concerning “cavitation”.

Keywords:

• Equations of viscous gas dynamics
• a priori estimates
• compensated compactness
• weak limit of solutions

AMS(MOS)::

• 35A05
• 35D05
• 35Q10
• 76N10
• 76N15