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Analyticity of the Stokes semigroup in spaces of bounded functions

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Acta Mathematica

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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  1. Graduate School of Mathematical Sciences, University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo, 153-8914, Japan

    Ken Abe & Yoshikazu Giga

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Abe, K., Giga, Y. Analyticity of the Stokes semigroup in spaces of bounded functions. Acta Math 211, 1–46 (2013). https://doi.org/10.1007/s11511-013-0098-6

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  • DOI: https://doi.org/10.1007/s11511-013-0098-6

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