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. denote by α friction coefficient and we analyze asymptotic behavior of such a as → ∞. More precisely, prove that if take each α, then there exists sequence controls converging to same Dirichlet condition. also show convergence corresponding direct adjoint states.