On the Heat Convection Equations with Dissipation Term in Regions with Moving Boundaries

We consider an initial value problem for a system of equations describing the motion and the heat convection in a viscous and incompressible fluid which occupies a smooth region Ω_t⊂ℝ³ depending on time. In the equation for the distribution of temperature in the fluid we take into account not only the convective term but also the term responsible for the dissipation of energy. We prove local in time existence and uniqueness of solutions of the considered problem, and global in time existence for sufficiently small data. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.