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Analyticity of the Stokes semigroup in spaces of bounded functions

Ken Abe Graduate School of Mathematical Sciences, University of Tokyo Yoshikazu Giga Graduate School of Mathematical Sciences, University of Tokyo

Functional Analysis Spectral Theory and Operator Algebra mathscidoc:1701.12004

Acta Mathematica, 211, (1), 1-46, 2011.7
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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@inproceedings{ken2011analyticity,
  title={Analyticity of the Stokes semigroup in spaces of bounded functions},
  author={Ken Abe, and Yoshikazu Giga},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203401288120775},
  booktitle={Acta Mathematica},
  volume={211},
  number={1},
  pages={1-46},
  year={2011},
}
Ken Abe, and Yoshikazu Giga. Analyticity of the Stokes semigroup in spaces of bounded functions. 2011. Vol. 211. In Acta Mathematica. pp.1-46. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203401288120775.
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