Neumann Problems for the Stokes Equations in Convex Domains
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909358911127552 |
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| author | Geng, Jun Shen, Zhongwei |
| author_facet | Geng, Jun Shen, Zhongwei |
| contents | This paper studies the Neumann boundary value problems for the Stokes equations in a convex domain in $\mathbb{R}^d$. We obtain nontangential-maximal-function estimates in $L^p$ and $W^{1, p}$ estimates for $p$ in certain ranges depending on $d$. These ranges are larger than the known ranges for Lipschitz domains. The proof relies on a $W^{2, 2}$ estimate for the Stokes equations in convex domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16650 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neumann Problems for the Stokes Equations in Convex Domains Geng, Jun Shen, Zhongwei Analysis of PDEs 35J57, 35Q35 This paper studies the Neumann boundary value problems for the Stokes equations in a convex domain in $\mathbb{R}^d$. We obtain nontangential-maximal-function estimates in $L^p$ and $W^{1, p}$ estimates for $p$ in certain ranges depending on $d$. These ranges are larger than the known ranges for Lipschitz domains. The proof relies on a $W^{2, 2}$ estimate for the Stokes equations in convex domains. |
| title | Neumann Problems for the Stokes Equations in Convex Domains |
| topic | Analysis of PDEs 35J57, 35Q35 |
| url | https://arxiv.org/abs/2410.16650 |