Well-posedness analysis of a stationary Navier–Stokes hemivariational inequality

Abstract This paper provides a well-posedness analysis for a hemivariational inequality of the stationary Navier-Stokes equations by arguments of convex minimization and the Banach fixed point. The hemivariational inequality describes a stationary incompressible fluid flow subject to a nonslip bound...

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Autores principales:	Min Ling, Weimin Han
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Hemivariational inequality Navier–Stokes equations Minimization principle Banach fixed point theorem Well-posedness Iteration method Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/63884540977f48beab59c1a0361eda8e
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spelling	oai:doaj.org-article:63884540977f48beab59c1a0361eda8e2021-12-05T12:10:30ZWell-posedness analysis of a stationary Navier–Stokes hemivariational inequality10.1186/s13663-021-00707-22730-5422https://doaj.org/article/63884540977f48beab59c1a0361eda8e2021-12-01T00:00:00Zhttps://doi.org/10.1186/s13663-021-00707-2https://doaj.org/toc/2730-5422Abstract This paper provides a well-posedness analysis for a hemivariational inequality of the stationary Navier-Stokes equations by arguments of convex minimization and the Banach fixed point. The hemivariational inequality describes a stationary incompressible fluid flow subject to a nonslip boundary condition and a Clarke subdifferential relation between the total pressure and the normal component of the velocity. Auxiliary Stokes hemivariational inequalities that are useful in proving the solution existence and uniqueness of the Navier–Stokes hemivariational inequality are introduced and analyzed. This treatment naturally leads to a convergent iteration method for solving the Navier–Stokes hemivariational inequality through a sequence of Stokes hemivariational inequalities. Equivalent minimization principles are presented for the auxiliary Stokes hemivariational inequalities which will be useful in developing numerical algorithms.Min LingWeimin HanSpringerOpenarticleHemivariational inequalityNavier–Stokes equationsMinimization principleBanach fixed point theoremWell-posednessIteration methodApplied mathematics. Quantitative methodsT57-57.97AnalysisQA299.6-433ENFixed Point Theory and Algorithms for Sciences and Engineering, Vol 2021, Iss 1, Pp 1-14 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Hemivariational inequality Navier–Stokes equations Minimization principle Banach fixed point theorem Well-posedness Iteration method Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
spellingShingle	Hemivariational inequality Navier–Stokes equations Minimization principle Banach fixed point theorem Well-posedness Iteration method Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433 Min Ling Weimin Han Well-posedness analysis of a stationary Navier–Stokes hemivariational inequality
description	Abstract This paper provides a well-posedness analysis for a hemivariational inequality of the stationary Navier-Stokes equations by arguments of convex minimization and the Banach fixed point. The hemivariational inequality describes a stationary incompressible fluid flow subject to a nonslip boundary condition and a Clarke subdifferential relation between the total pressure and the normal component of the velocity. Auxiliary Stokes hemivariational inequalities that are useful in proving the solution existence and uniqueness of the Navier–Stokes hemivariational inequality are introduced and analyzed. This treatment naturally leads to a convergent iteration method for solving the Navier–Stokes hemivariational inequality through a sequence of Stokes hemivariational inequalities. Equivalent minimization principles are presented for the auxiliary Stokes hemivariational inequalities which will be useful in developing numerical algorithms.
format	article
author	Min Ling Weimin Han
author_facet	Min Ling Weimin Han
author_sort	Min Ling
title	Well-posedness analysis of a stationary Navier–Stokes hemivariational inequality
title_short	Well-posedness analysis of a stationary Navier–Stokes hemivariational inequality
title_full	Well-posedness analysis of a stationary Navier–Stokes hemivariational inequality
title_fullStr	Well-posedness analysis of a stationary Navier–Stokes hemivariational inequality
title_full_unstemmed	Well-posedness analysis of a stationary Navier–Stokes hemivariational inequality
title_sort	well-posedness analysis of a stationary navier–stokes hemivariational inequality
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/63884540977f48beab59c1a0361eda8e
work_keys_str_mv	AT minling wellposednessanalysisofastationarynavierstokeshemivariationalinequality AT weiminhan wellposednessanalysisofastationarynavierstokeshemivariationalinequality
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Well-posedness analysis of a stationary Navier–Stokes hemivariational inequality

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