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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2401.03222 |
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| _version_ | 1866917738388127744 |
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| author | Geng, Jun Shen, Zhongwei |
| author_facet | Geng, Jun Shen, Zhongwei |
| contents | We establish resolvent estimates in $L^q$ spaces for the Stokes operator in a bounded $C^1$ domain $Ω$ in $\mathbb{R}^d$. As a corollary, it follows that the Stokes operator generates a bounded analytic semigroup in $L^q(Ω; \mathbb{C}^d)$ for any $1< q< \infty$ and $d\ge 2$. The case of an exterior $C^1$ domain is also studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03222 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Resolvent Estimates for the Stokes Operator in Bounded and Exterior $C^1$ Domains Geng, Jun Shen, Zhongwei Analysis of PDEs 35Q30 We establish resolvent estimates in $L^q$ spaces for the Stokes operator in a bounded $C^1$ domain $Ω$ in $\mathbb{R}^d$. As a corollary, it follows that the Stokes operator generates a bounded analytic semigroup in $L^q(Ω; \mathbb{C}^d)$ for any $1< q< \infty$ and $d\ge 2$. The case of an exterior $C^1$ domain is also studied. |
| title | Resolvent Estimates for the Stokes Operator in Bounded and Exterior $C^1$ Domains |
| topic | Analysis of PDEs 35Q30 |
| url | https://arxiv.org/abs/2401.03222 |