Preprint
On Well-posedness of a Nonstationary Stokes Hemivariational Inequality
ArXiv.org
Cornell University
03/28/2026
DOI: 10.48550/arxiv.2603.27388
Abstract
This paper is devoted to the well-posedness analysis of a nonstationary Stokes hemivariational inequality for an incompressible fluid flow described by the Stokes equations subject to a nonsmooth boundary condition of friction type described by the Clarke subdifferential. In a recent paper [19], well-posedness of the nonstationary Stokes hemivariational inequality is studied for both the velocity and pressure fields. The solution existence is shown through a limiting procedure based on temporally semi-discrete approximations for both the velocity and pressure fields. In this paper, a refined well-posedness analysis is provided on the nonstationary Stokes hemivariational inequality under more natural assumptions on the problem data. The solution existence is first shown for the velocity field through a limiting procedure based on temporally semi-discrete approximations of a reduced problem and then the pressure field is recovered with the help of an inf-sup property. In this way, assumptions on the source term and the initial velocity needed in [19] are weakened, and a compatibility condition on initial values of the data is dropped. Moreover, several hemivariational inequalities are introduced for the mathematical model and their equivalence is explored.
Details
- Title: Subtitle
- On Well-posedness of a Nonstationary Stokes Hemivariational Inequality
- Creators
- Weimin HanShengda Zeng
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2603.27388
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 03/28/2026
- Academic Unit
- Mathematics
- Record Identifier
- 9985149572602771
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