Analyticity of the Stokes semigroup in spaces of bounded functions

2013/01/01 by Ken Abe, Yoshikazu Giga · 3 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Stability and Controllability of Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.1007/s11511-013-0098-6

Abstract

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.

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