Heat Convection Equation with Nonhomogeneous Boundary Condition

Abstract

We consider the stationary heat convection equations and the time periodic heat convection equations (Boussinesq approximation) with non-homogeneous boundary condition, and obtain the existence result similar to the Navier-Stokes equations' case.
The boundary value for the fluid velocity should satisfy so-called general outflow condition (GOC). For the 2 or 3 dimensional bounded domain, the existence of the solution can be shown if the boundary condition satisfies the stringent outflow condition (SOC). Similarly to the Navier-Stokes equations, we obtain the existence result for the 2 dimensional symmetric domain and symmetric data with the boundary value satisfying only (GOC).