Resolvent Estimates for the Stokes Operator in Bounded and Exterior $C^1$ Domains
Jun Geng, Zhongwei Shen · arXiv (Cornell University) · 2024
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.