OPTIMAL-CONTROL OF A NON ISOTHERMAL NAVIER-STOKES FLOW

This paper deals with a boundary optimal control problem associated wi th the stationary Navier-Stokes equations coupled with the heat equati on. The most general type of boundary condition for the temperature is considered. The existence of a solution of this problem and, for some values of the viscosity coefficient, the uniqueness are proved. The c ontrol problem consists in finding a temperature of the surrounding me dium which leads to a desired configuration of the temperature of the fluid. The existence of an optimal control is proved and necessary con ditions of optimality are derived by introducing a family of regulariz ed optimal problems.