Optimal control of fluid equations with buoyancy

摘要

We consider the optimal control of a set of fluid equations made up of the momentum equations coupled with an equation modeling thermal effects. Control is exerted by means of heat sources within the fluid with the goal of controlling the temperature or velocity distribution of the fluid. Existence as well as the regularity properties of optimal controls are analyzed. Stability with respect to observations is discussed. Finally, compactness of the solution set and uniqueness properties are determined.