Global weak solutions to a class of non-Newtonian compressible fluids

Abstract

We consider a class of compressible fluids with nonlinear constitutive equations that guarantee that the divergence of the velocity field remains bounded. We study mathematical properties of unsteady three-dimensional flows of such fluids in bounded domains.

In particular, we show the long-time and large-data existence result of weak solutions with strictly positive density.

Keywords

• compressible fluid
• generalized Newtonian fluids
• power law fluid
• bounded divergence of the velocity
• weak solutions
• positive density