Bounded 𝐻^{∞}-calculus for the hydrostatic Stokes operator on 𝐿^{𝑝}-spaces and applications

Giga, Yoshikazu; Gries, Mathis; Hieber, Matthias; Hussein, Amru; Kashiwabara, Takahito

doi:10.1090/proc/13676

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.

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