QUASI-VARIATIONAL INEQUALITY APPROACH TO HEAT CONVECTION PROBLEMS WITH TEMPERATURE DEPENDENT VELOCITY CONSTRAINT

摘要

This paper is concerned with a heat convection problem. We discuss it in the framework of parabolic variational inequalities. The problem is a system of a heat equation with convection and a Navier-Stokes variational inequality with temperature-dependent velocity constraint. Our problem is a sort of parabolic quasi-variational inequalities in the sense that the constraint set for the velocity field depends on the unknown temperature. We shall give an existence result of the heat convection problem in a weak sense, and show that under some additional constraint for temperature there exists a strong solution of the problem.