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

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.

Automated summary

In this study, we investigated the optimal control problem of the Navier-Stokes system with Navier slip boundary conditions. We analyzed the asymptotic behavior of the problem when the friction coefficient a tends to 0.8. The results showed that by choosing an optimal control for each a, we can obtain a sequence of optimal controls that converge to the optimal control problem of the Navier-Stokes system with Dirichlet boundary conditions. We also demonstrated the convergence of the corresponding direct and adjoint states.