Shape optimization for the Stokes system with threshold leak boundary conditions

This paper discusses the process of optimizing the shape of systems that are controlled by the Stokes flow with threshold leak boundary conditions. In the theoretical part it focuses on studying the stability of solutions to the state problem in relation to a specific set of domains. In order to facilitate computation, the slip term and impermeability condition are regulated. In the computational part, the optimized portion of the boundary is defined using Bézier polynomials, in order to create a finite dimensional optimization problem. The paper also includes numerical examples to demonstrate the computational efficiency of this approach.