Existence and Uniqueness Results for Viscous, Heat-conducting 3-D Fluid with Vacuum

Abstract

We prove the local existence and uniqueness of the strong solution to the 3-D full Navier-Stokes equations whose the viscosity coefficients and the thermal conductivity coefficient depend on the density and the temperature. The initial density may vanish in an open set and the domain could be bounded or unbounded. Finally, we show the blow-up of the smooth solution to the compressible Navier-Stokes equations in R^n (n ≥ 1) when the initial density has compactly support and the initial total momentum is nonzero.