Nonstationary Stokes equations on a domain with curved boundary under slip boundary conditions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909462333227008 |
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| author | Dong, Hongjie Kwon, Hyunwoo |
| author_facet | Dong, Hongjie Kwon, Hyunwoo |
| contents | We consider nonstationary Stokes equations in nondivergence form with variable viscosity coefficients and generalized Navier slip boundary conditions with slip tensor $\mathcal{A}$ in a domain $Ω$ in $\mathbb{R}^d$. First, under the assumption that slip matrix $\mathcal{A}$ is sufficiently smooth, we establish a priori local regularity estimates for solutions near a curved portion of the domain boundary. Second, when $\mathcal{A}$ is the shape operator, we derive local boundary estimates for the Hessians of the solutions, where the right-hand side does not involve the pressure. Notably, our results are new even if the viscosity coefficients are constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_17321 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonstationary Stokes equations on a domain with curved boundary under slip boundary conditions Dong, Hongjie Kwon, Hyunwoo Analysis of PDEs 76D03, 76D07, 35K51, 35B45 We consider nonstationary Stokes equations in nondivergence form with variable viscosity coefficients and generalized Navier slip boundary conditions with slip tensor $\mathcal{A}$ in a domain $Ω$ in $\mathbb{R}^d$. First, under the assumption that slip matrix $\mathcal{A}$ is sufficiently smooth, we establish a priori local regularity estimates for solutions near a curved portion of the domain boundary. Second, when $\mathcal{A}$ is the shape operator, we derive local boundary estimates for the Hessians of the solutions, where the right-hand side does not involve the pressure. Notably, our results are new even if the viscosity coefficients are constant. |
| title | Nonstationary Stokes equations on a domain with curved boundary under slip boundary conditions |
| topic | Analysis of PDEs 76D03, 76D07, 35K51, 35B45 |
| url | https://arxiv.org/abs/2408.17321 |