Journal article
A class of hemivariational inequalities for nonstationary Navier–Stokes equations
Nonlinear analysis: real world applications, Vol.31, pp.257-276
10/2016
DOI: 10.1016/j.nonrwa.2016.02.005
Abstract
This paper is devoted to the study of a class of hemivariational inequalities for the time-dependent Navier–Stokes equations, including both boundary hemivariational inequalities and domain hemivariational inequalities. The hemivariational inequalities are analyzed in the framework of an abstract hemivariational inequality. Solution existence for the abstract hemivariational inequality is explored through a limiting procedure for a temporally semi-discrete scheme based on the backward Euler difference of the time derivative, known as the Rothe method. It is shown that solutions of the Rothe scheme exist, they contain a weakly convergent subsequence as the time step-size approaches zero, and any weak limit of the solution sequence is a solution of the abstract hemivariational inequality. It is further shown that under certain conditions, a solution of the abstract hemivariational inequality is unique and the solution of the abstract hemivariational inequality depends continuously on the problem data. The results on the abstract hemivariational inequality are applied to hemivariational inequalities associated with the time-dependent Navier–Stokes equations.
Details
- Title: Subtitle
- A class of hemivariational inequalities for nonstationary Navier–Stokes equations
- Creators
- Changjie Fang - Chongqing University of Posts and TelecommunicationsWeimin Han - Xi'an Jiaotong UniversityStanisław Migórski - Jagiellonian UniversityMircea Sofonea - Université de Perpignan
- Resource Type
- Journal article
- Publication Details
- Nonlinear analysis: real world applications, Vol.31, pp.257-276
- DOI
- 10.1016/j.nonrwa.2016.02.005
- ISSN
- 1468-1218
- eISSN
- 1878-5719
- Publisher
- Elsevier Ltd
- Grant note
- W111/7.PR/2012 / Ministry of Science and Higher Education of Republic of Poland (http://dx.doi.org/10.13039/501100004569) 207052 / Simons Foundation (http://dx.doi.org/10.13039/100000893) cstc2014jcyjA00044 / Basic and Advanced Research Project of CQ CSTC DMS-1521684 / NSF (http://dx.doi.org/10.13039/100000001) 11426055 / National Natural Science Foundation of China (http://dx.doi.org/10.13039/501100001809) Marie Curie International Research Staff Exchange Scheme Fellowship DEC-2012/06/A/ST1/00262 / National Science Center of Poland under the Maestro Advanced Project (http://dx.doi.org/10.13039/501100004281) 295118 / 7th European Community Framework Programme (http://dx.doi.org/10.13039/501100004963)
- Language
- English
- Date published
- 10/2016
- Academic Unit
- Mathematics
- Record Identifier
- 9984240768202771
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