Bounded H∞-calculus for the hydrostatic stokes operator on Lp-spaces and applications

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

doi:10.1090/proc/13676

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

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

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

It is shown that the hydrostatic Stokes operator on Lp/σ(Ω), where Ω ⊂ ℝ³ is a cylindrical domain subject to mixed periodic, Dirichlet and Neumann boundary conditions, admits a bounded H^∞-calculus on Lp/σ(Ω) for p ∈ (1, ∞) of H^∞-angle 0. In particular, maximal L^q − L^p-regularity estimates for the linearized primitive equations are obtained.

Original language	English
Pages (from-to)	3865-3876
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	145
Issue number	9
DOIs	https://doi.org/10.1090/proc/13676
Publication status	Published - 2017
Externally published	Yes

Keywords

H-functional calculus
Hydrostatic Stokes operator
Maximal L-regularity

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/proc/13676

Cite this

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abstract = "It is shown that the hydrostatic Stokes operator on Lp/σ(Ω), where Ω ⊂ ℝ3 is a cylindrical domain subject to mixed periodic, Dirichlet and Neumann boundary conditions, admits a bounded H∞-calculus on Lp/σ(Ω) for p ∈ (1, ∞) of H∞-angle 0. In particular, maximal Lq − Lp-regularity estimates for the linearized primitive equations are obtained.",

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AU - Giga, Yoshikazu

AU - Gries, Mathis

AU - Hieber, Matthias Georg

AU - Hussein, Amru

AU - Kashiwabara, Takahito

PY - 2017

Y1 - 2017

N2 - It is shown that the hydrostatic Stokes operator on Lp/σ(Ω), where Ω ⊂ ℝ3 is a cylindrical domain subject to mixed periodic, Dirichlet and Neumann boundary conditions, admits a bounded H∞-calculus on Lp/σ(Ω) for p ∈ (1, ∞) of H∞-angle 0. In particular, maximal Lq − Lp-regularity estimates for the linearized primitive equations are obtained.

AB - It is shown that the hydrostatic Stokes operator on Lp/σ(Ω), where Ω ⊂ ℝ3 is a cylindrical domain subject to mixed periodic, Dirichlet and Neumann boundary conditions, admits a bounded H∞-calculus on Lp/σ(Ω) for p ∈ (1, ∞) of H∞-angle 0. In particular, maximal Lq − Lp-regularity estimates for the linearized primitive equations are obtained.

KW - H-functional calculus

KW - Hydrostatic Stokes operator

KW - Maximal L-regularity

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