Injection-suction control for Navier-Stokes equations with slippage

Abstract

We consider a velocity tracking problem for the Navier-Stokes equations in a 2D-bounded domain. The control acts on the boundary through a injection-suction device and the flow is allowed to slip against the surface wall. We study the well-posedness of the state equations, linearized state equations and adjoint equations. In addition, we show the existence of an optimal solution and establish the first order optimality condition.

arXiv comment23 pages

References in corpus (1)

• Slip behavior in liquid films on surfaces of patterned wettability: Comparison between continuum and molecular dynamics simulations