Analysis of Stokes system with solution-dependent subdifferential boundary conditions

Abstract We study the Stokes problem for the incompressible fluid with mixed nonlinear boundary conditions of subdifferential type. The latter involve a unilateral boundary condition, the Navier slip condition, a nonmonotone version of the nonlinear Navier–Fujita slip condition, and the threshold sl...

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Autores principales:	Jing Zhao, Stanisław Migórski, Sylwia Dudek
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Stokes problem Variational–hemivariational inequality Generalized subgradient Leak and slip condition Unilateral boundary condition Fixed point Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/afe2cd3226f54069afec2a37403266b6
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spelling	oai:doaj.org-article:afe2cd3226f54069afec2a37403266b62021-11-14T12:15:49ZAnalysis of Stokes system with solution-dependent subdifferential boundary conditions10.1186/s13663-021-00704-52730-5422https://doaj.org/article/afe2cd3226f54069afec2a37403266b62021-11-01T00:00:00Zhttps://doi.org/10.1186/s13663-021-00704-5https://doaj.org/toc/2730-5422Abstract We study the Stokes problem for the incompressible fluid with mixed nonlinear boundary conditions of subdifferential type. The latter involve a unilateral boundary condition, the Navier slip condition, a nonmonotone version of the nonlinear Navier–Fujita slip condition, and the threshold slip and leak condition of frictional type. The weak form of the problem leads to a new class of variational–hemivariational inequalities on convex sets for the velocity field. Solution existence and the weak compactness of the solution set to the inequality problem are established based on the Schauder fixed point theorem.Jing ZhaoStanisław MigórskiSylwia DudekSpringerOpenarticleStokes problemVariational–hemivariational inequalityGeneralized subgradientLeak and slip conditionUnilateral boundary conditionFixed pointApplied mathematics. Quantitative methodsT57-57.97AnalysisQA299.6-433ENFixed Point Theory and Algorithms for Sciences and Engineering, Vol 2021, Iss 1, Pp 1-18 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Stokes problem Variational–hemivariational inequality Generalized subgradient Leak and slip condition Unilateral boundary condition Fixed point Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
spellingShingle	Stokes problem Variational–hemivariational inequality Generalized subgradient Leak and slip condition Unilateral boundary condition Fixed point Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433 Jing Zhao Stanisław Migórski Sylwia Dudek Analysis of Stokes system with solution-dependent subdifferential boundary conditions
description	Abstract We study the Stokes problem for the incompressible fluid with mixed nonlinear boundary conditions of subdifferential type. The latter involve a unilateral boundary condition, the Navier slip condition, a nonmonotone version of the nonlinear Navier–Fujita slip condition, and the threshold slip and leak condition of frictional type. The weak form of the problem leads to a new class of variational–hemivariational inequalities on convex sets for the velocity field. Solution existence and the weak compactness of the solution set to the inequality problem are established based on the Schauder fixed point theorem.
format	article
author	Jing Zhao Stanisław Migórski Sylwia Dudek
author_facet	Jing Zhao Stanisław Migórski Sylwia Dudek
author_sort	Jing Zhao
title	Analysis of Stokes system with solution-dependent subdifferential boundary conditions
title_short	Analysis of Stokes system with solution-dependent subdifferential boundary conditions
title_full	Analysis of Stokes system with solution-dependent subdifferential boundary conditions
title_fullStr	Analysis of Stokes system with solution-dependent subdifferential boundary conditions
title_full_unstemmed	Analysis of Stokes system with solution-dependent subdifferential boundary conditions
title_sort	analysis of stokes system with solution-dependent subdifferential boundary conditions
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/afe2cd3226f54069afec2a37403266b6
work_keys_str_mv	AT jingzhao analysisofstokessystemwithsolutiondependentsubdifferentialboundaryconditions AT stanisławmigorski analysisofstokessystemwithsolutiondependentsubdifferentialboundaryconditions AT sylwiadudek analysisofstokessystemwithsolutiondependentsubdifferentialboundaryconditions
_version_	1718429367126720512

Analysis of Stokes system with solution-dependent subdifferential boundary conditions

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