Resolvent estimates in L∞ for the Stokes operator in nonsmooth domains

• 成果类型: Article; Early Access
• 署名作者: Geng, Jun; Shen, Zhongwei
• 署名单位: Lanzhou University; Westlake University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01383-4
• 发表日期: 2025
• 关键词: dirichlet problem; semigroup; EQUATIONS; analyticity; REGULARITY; systems; SPACES

摘要

We establish resolvent estimates in spaces of bounded solenoidal functions for the Stokes operator in a bounded domain Omega in Rd under the assumptions that Omega is C1 for d >= 3 and Lipschitz for d=2. As a corollary, it follows that the Stokes operator generates a uniformly bounded analytic semigroup in the spaces of bounded solenoidal functions in Omega. The smoothness conditions on Omega are sharp. The case of exterior domains with nonsmooth boundaries is also studied. The key step in our proof involves new estimates that connect the pressure to the gradient of the velocity in the Lq average, but only on scales above certain level.