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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2603.27388 |
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| _version_ | 1866918414718599168 |
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| author | Han, Weimin Zeng, Shengda |
| author_facet | Han, Weimin Zeng, Shengda |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27388 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Well-posedness of a Nonstationary Stokes Hemivariational Inequality Han, Weimin Zeng, Shengda Numerical Analysis 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. |
| title | On Well-posedness of a Nonstationary Stokes Hemivariational Inequality |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.27388 |