Resolvent Estimates for the Stokes Operator in Bounded and Exterior C¹ Domains

2024/01/06 by Geng, Jun, Shen, Zhongwei
#35Q30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.03222

Abstract

We establish resolvent estimates in L^q spaces for the Stokes operator in a bounded C¹ domain Ω in ℝ^d. As a corollary, it follows that the Stokes operator generates a bounded analytic semigroup in L^q(Ω; ℂ^d) for any 1< q< ∞ and d≥ 2. The case of an exterior C¹ domain is also studied.

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