Bounded $H^{\infty }$-calculus for the hydrostatic Stokes operator on $L^p$-spaces and applications
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- by Yoshikazu Giga, Mathis Gries, Matthias Hieber, Amru Hussein and Takahito Kashiwabara PDF
- Proc. Amer. Math. Soc. 145 (2017), 3865-3876 Request permission
Abstract:
It is shown that the hydrostatic Stokes operator on $L^p_{\overline {\sigma }}(\Omega )$, where $\Omega \subset \mathbb {R}^3$ is a cylindrical domain subject to mixed periodic, Dirichlet and Neumann boundary conditions, admits a bounded $H^\infty$-calculus on $L^p_{\overline {\sigma }}(\Omega )$ for $p\in (1,\infty )$ of $H^\infty$-angle $0$. In particular, maximal $L^q-L^p$-regularity estimates for the linearized primitive equations are obtained.References
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Additional Information
- Yoshikazu Giga
- Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
- MR Author ID: 191842
- Email: labgiga@ms.u-tokyo.ac.jp
- Mathis Gries
- Affiliation: Departement of Mathematics, TU Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany
- Email: gries@mathematik.tu-darmstadt.de
- Matthias Hieber
- Affiliation: Departement of Mathematics, TU Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany
- MR Author ID: 270487
- Email: hieber@mathematik.tu-darmstadt.de
- Amru Hussein
- Affiliation: Departement of Mathematics, TU Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany
- MR Author ID: 1023773
- Email: hussein@mathematik.tu-darmstadt.de
- Takahito Kashiwabara
- Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
- MR Author ID: 997963
- Email: tkashiwa@ms.u-tokyo.ac.jp
- Received by editor(s): July 1, 2016
- Received by editor(s) in revised form: August 2, 2016
- Published electronically: May 24, 2017
- Additional Notes: This work was partly supported by the DFG International Research Training Group IRTG 1529 and the JSPS Japanese-German Graduate Externship on Mathematical Fluid Dynamics.
The first author is partly supported by JSPS through grant Kiban S (No. 26220702).
The second and fourth authors are supported by IRTG 1529 at TU Darmstadt - Communicated by: Joachim Krieger
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3865-3876
- MSC (2010): Primary 35Q35; Secondary 47D06, 76D03
- DOI: https://doi.org/10.1090/proc/13676
- MathSciNet review: 3665039