THE BOUSSINESQ SYSTEM WITH NONSMOOTH BOUNDARY CONDITIONS: EXISTENCE, RELAXATION, AND TOPOLOGY OPTIMIZATION.

In this paper, we tackle a topology optimization problem which consists in finding the optimal shape of a solid located inside a fluid that minimizes a given cost function. The motion of the fluid is modeled thanks to the Boussinesq system which involves the unsteady Navier-Stokes equation coupled with a heat equation. In order to cover several models presented in the literature, we choose a nonsmooth formulation for the outlet boundary conditions. This paper aims at proving the existence of solutions to the resulting equations, along with the study of a relaxation scheme of the nonsmooth conditions. A second part covers the topology optimization problem itself for which we proved the existence of optimal solutions and provides the definition of first order necessary optimality conditions. [ABSTRACT FROM AUTHOR]