Well-posedness and optimal control of a hemivariational inequality for nonstationary Stokes fluid flow

Changjie  Fang; Weimin  Han

doi:10.3934/dcds.2016036

Article Contents

2016, Volume 36, Issue 10: 5369-5386. Doi: 10.3934/dcds.2016036

This issue Previous Article Periodic and eventually periodic points of affine infra-nilmanifold endomorphisms Next Article On uniform in time $H^2$-regularity of the solution for the 2D Cahn-Hilliard equation

Well-posedness and optimal control of a hemivariational inequality for nonstationary Stokes fluid flow

Changjie Fang^1, and
Weimin Han^2,

1.
College of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065
2.
Department of Mathematics, University of Iowa, Iowa City, IA 52242

Received: August 2015

Revised: April 2016

Published: May 2017

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Abstract

A time-dependent Stokes fluid flow problem is studied with nonlinear boundary conditions described by the Clarke subdifferential. We present equivalent weak formulations of the problem, one of them in the form of a hemivariational inequality. The existence of a solution is shown through a limiting procedure based on temporally semi-discrete approximations. Uniqueness of the solution and its continuous dependence on data are also established. Finally, we present a result on the existence of a solution to an optimal control problem for the hemivariational inequality.

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Mathematics Subject Classification: Primary: 35A15, 35A35; Secondary: 49J20.

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