A regularization of incompressible Stokes problem with Tresca friction condition
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913713011818496 |
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| author | Zafrar, A. |
| author_facet | Zafrar, A. |
| contents | In the present article, we introduce and study a model addressing the Stokes problem with non-linear boundary conditions of the Tresca type. We suggest a new procedure for regularizing incompressible fluid, i.e. we assume that the divergence $\nabla \cdot {\bf u}\in [-ε,\,ε]$ which leads to class of constrained elliptic variational inequalities. We use a fixed point strategy to show the existence and uniqueness of a solution and we reformulate the problem as an equivalent constrained minimization problem. An ADMM is applied to the minimization problem and some algorithm are provided. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_00158 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A regularization of incompressible Stokes problem with Tresca friction condition Zafrar, A. Analysis of PDEs Numerical Analysis In the present article, we introduce and study a model addressing the Stokes problem with non-linear boundary conditions of the Tresca type. We suggest a new procedure for regularizing incompressible fluid, i.e. we assume that the divergence $\nabla \cdot {\bf u}\in [-ε,\,ε]$ which leads to class of constrained elliptic variational inequalities. We use a fixed point strategy to show the existence and uniqueness of a solution and we reformulate the problem as an equivalent constrained minimization problem. An ADMM is applied to the minimization problem and some algorithm are provided. |
| title | A regularization of incompressible Stokes problem with Tresca friction condition |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2503.00158 |