The Strong Solution for the Viscous Polytropic Fluids with Non-Newtonian Potential

Abstract

The authors study an initial boundary value problem for the three-dimensional Navier-Stokes equations of viscous heat-conductive fluids with non-Newtonian potential in a bounded smooth domain. They prove the existence of unique local strong solutions for all initial data satisfying some compatibility conditions. The difficult of this type model is mainly that the equations are coupled with elliptic, parabolic and hyperbolic, and the vacuum of density causes also much trouble, that is, the initial density need not be positive and may vanish in an open set.

Keywords

Compressible Navier-Stokes equations / Viscous polytropic fluids / Vacuum / Poincaré type inequality / Non-Newtonian potential

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