Logo image
Minimization principle in study of a Stokes hemivariational inequality
Journal article   Peer reviewed

Minimization principle in study of a Stokes hemivariational inequality

Min Ling and Weimin Han
Applied mathematics letters, Vol.121, p.107401
11/2021
DOI: 10.1016/j.aml.2021.107401

View Online

Abstract

In this paper, an equivalent minimization principle is established for a hemivariational inequality of the stationary Stokes equations with a nonlinear slip boundary condition. Under certain assumptions on the data, it is shown that there is a unique minimizer of the minimization problem, and furthermore, the mixed formulation of the Stokes hemivariational inequality has a unique solution. The proof of the result is based on basic knowledge of convex minimization. For comparison, in the existing literature, the solution existence and uniqueness result for the Stokes hemivariational inequality is proved through the notion of pseudomonotonicity and an application of an abstract surjectivity result for pseudomonotone operators, in which an additional linear growth condition is required on the subdifferential of a super-potential in the nonlinear slip boundary condition.
Existence Hemivariational inequality Minimization principle Stokes equations Uniqueness

Details

Metrics

Logo image