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We consider a velocity tracking problem for the Navier-Stokes equations in a2D-bounded domain. The control acts on the boundary through a injection-suctiondevice and the flow is allowed to slip against the surface wall. We study thewell-posedness of the state equations, linearized state equations and adjointequations. In addition, we show the existence of an optimal solution andestablish the first order optimality condition.

Injection-suction control for Navier-Stokes equations with slippage