Continuity equation and vacuum regions in compressible flows

Abstract

We investigate the creation and properties of eventual vacuum regions in the weak solutions of the continuity equation, in general, and in the weak solutions of compressible Navier-Stokes equations, in particular. The main results are based on the analysis of renormalized solutions to the continuity and pure transport equations and their inter-relations which are of independent interest.

Keywords

• compressible Navier-Stokes equations
• vacuum regions
• renormalized solution
• transport equation
• continuity equation