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The L ∞-Stokes semigroup in exterior domains

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Abstract

The Stokes semigroup on a bounded domain is an analytic semigroup on spaces of bounded functions as was recently shown by the authors based on an a priori L ∞-estimate for solutions to the linear Stokes equations. In this paper, we extend our approach to exterior domains and prove that the Stokes semigroup is uniquely extendable to an analytic semigroup on spaces of bounded functions.

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Authors and Affiliations

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

    Ken Abe & Yoshikazu Giga

  2. Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia

    Yoshikazu Giga

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  1. Ken Abe
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  2. Yoshikazu Giga
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Correspondence to Ken Abe.

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Abe, K., Giga, Y. The L ∞-Stokes semigroup in exterior domains. J. Evol. Equ. 14, 1–28 (2014). https://doi.org/10.1007/s00028-013-0197-z

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