# American Institute of Mathematical Sciences

doi: 10.3934/eect.2020046

## Stability analysis and optimal control of A stationary Stokes hemivariational inequality

 1 College of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China 2 Key Lab of Intelligent Analysis and Decision on Complex Systems, Chongqing University of Posts and Telecommunications, Chongqing 400065, China 3 Department of Mathematics, University of Iowa, Iowa City, IA 52242-1410, USA

* Corresponding author: Weimin Han

Dedicated to Professor Meir Shillor on the occasion of his 70th birthday

Received  October 2019 Published  March 2020

Fund Project: The first author is supported by the National Natural Science Foundation of China (No. 11771350), Basic and Advanced Research Project of CQ CSTC (Nos. cstc2016jcyjA0163 and cstc2018jcyjAX0605)

In this paper, we provide stability analysis for a stationary Stokes hemivariational inequality where along the tangential direction of the slip boundary, an inclusion relation involving the generalized subdifferential of a superpotential is specified. With viscous incompressible fluid flows as application background, stability is analyzed for solutions with respect to perturbations in the superpotential and the density of external forces. We also present a result on the existence of a solution to an optimal control problem for the stationary Stokes hemivariational inequality.

Citation: Changjie Fang, Weimin Han. Stability analysis and optimal control of A stationary Stokes hemivariational inequality. Evolution Equations & Control Theory, doi: 10.3934/eect.2020046
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