A note on optimal control problem for a hemivariational inequality modeling fluid flow

Pages: 545 - 554, Issue special, November 2013

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Stanisław Migórski - Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. Łojasiewicza 6, 30348 Krakow, Poland (email)

Abstract: We consider a class of distributed parameter optimal control problems for the boundary value problem for the stationary Navier--Stokes equation with a subdifferential boundary condition in a bounded domain. The weak formulation of the boundary value problem is a hemivariational inequality associated with a nonconvex nonsmooth locally Lipschitz superpotential. We establish the existence of solutions to the optimal control problem. We also address an open problem of potential identification in the hemivariational inequality.

Keywords:  Optimal control, Navier-Stokes equation, hemivariational inequality, Clarke subdifferential, pseudomonotone, nonconvex, operator inclusion, weak solution.
Mathematics Subject Classification:  Primary: 35Q30, 76D05, 35J87, 49J20, 49J52.

Received: October 2012; Published: November 2013.