Existence result for heat-conducting viscous incompressible fluids with vacuum

Preprint Series # 742
Cho, Yonggeun and Kim, Hyunseok Existence result for heat-conducting viscous incompressible fluids with vacuum. (2005);

 TeX DVI190Kb

Abstract

We study the Navier-Stokes equations for heat-conducting incompressible fluids in a domain $\Omega \subset \mathbf{R}^3$ whose viscosity, heat conduction coefficients and specific heat at constant volume are in general functions of density and temperature. We prove the local existence of the unique strong solution, provided the initial data satisfy a natural compatibility condition. For the strong regularity, we do not assume the positivity of initial density; it may vanish in an open subset (vacuum) of $\Omega$ or decay at infinity when $\Omega$ is unbounded.

Item Type: Preprint 10 heat-conducting incompressible Navier-Stokes equations, strong solutions, vacuum 35-xx PARTIAL DIFFERENTIAL EQUATIONS 1056