Analyticity of the Stokes semigroup in spaces of bounded functions

• 成果类型: Article
• 署名作者: Abe, Ken; Giga, Yoshikazu
• 署名单位: University of Tokyo
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-013-0098-6
• 发表日期: 2013
• 页码: 1-46
• 关键词: variable viscosity; operator; DECOMPOSITION; generation; EXISTENCE; EQUATIONS; SYSTEM; FLOW

摘要

The analyticity of the Stokes semigroup with the Dirichlet boundary condition is established in spaces of bounded functions when the domain occupied with fluid is bounded or more generally admissible which admits a special estimate for the Helmholtz decomposition. The proof is based on a blow-up argument. This is the first proof of the analyticity in spaces of bounded functions which was left open more than thirty years.