Large Data Existence Result for Unsteady Flows of Inhomogeneous Shear-Thickening Heat-Conducting Incompressible Fluids

Abstract

We consider unsteady flows of inhomogeneous, incompressible, shear-thickening and heat-conducting fluids where the viscosity depends on the density, the temperature and the shear rate, and the heat conductivity depends on the temperature and the density. For any values of initial total mass and initial total energy we establish the long-time existence of weak solution to internal flows inside an arbitrary bounded domain with Lipschitz boundary.