Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

摘要

We consider an optimal control problem for the Navier-Stokes system with Navier slip boundary conditions. We denote by a the friction coefficient and we analyze the asymptotic behavior of such a problem as a.8. More precisely, we prove that if we take an optimal control for each a, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier-Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.