Strong Solutions for Nonhomogeneous Incompressible Viscous Heat-Conductive Fluids with Non-Newtonian Potential

Abstract

" We consider the Navier-Stokes system with non-Newtonian potential for heat-conducting incompressible fluids in a domain \u03a9\u2282\u211c^3. The viscosity, heat conduction coefficients and specific heat at constant volume are allowed to depend smoothly on the density and temperature. We prove the existence of unique local strong solutions for all initial data satisfying a natural compatibility condition. The difficult of this type model is mainly that the equations are coupled with elliptic, parabolic and hyperbolic, and the vacuum of density cause also much trouble, that is, the initial density need not be positive and may vanish in an open set."