Injection-suction control for Navier-Stokes equations with slippage

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...

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Bibliographic Details
Published in:arXiv.org 2017-06
Main Authors: Chemetov, Nikolai V, Cipriano, Fernanda
Format: Article
Language:English
Subjects:
Equations of state
Fluid dynamics
Fluid flow
Mathematical analysis
Navier-Stokes equations
Optimization
Slippage
Suction
Tracking problem
Well posed problems
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Summary: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.
ISSN:2331-8422