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arXiv · 2401.03222

Resolvent Estimates for the Stokes Operator in Bounded and Exterior $C^1$ Domains

Jun Geng·Zhongwei Shen
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Abstract

We establish resolvent estimates in $L^q$ spaces for the Stokes operator in a bounded $C^1$ domain $\Omega$ in $\mathbb{R}^d$. As a corollary, it follows that the Stokes operator generates a bounded analytic semigroup in $L^q(\Omega; \mathbb{C}^d)$ for any $1< q< \infty$ and $d\ge 2$. The case of an exterior $C^1$ domain is also studied.

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Jun Geng, Zhongwei Shen. 2024-01-06. Resolvent Estimates for the Stokes Operator in Bounded and Exterior $C^1$ Domains. https://arxiv.org/abs/2401.03222

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