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

DOI10.1090/proc/13676zbMath1480.35323OpenAlexW2589250995MaRDI QIDQ5274744

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

Publication date: 6 July 2017

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13676

zbMATH Keywords

maximal \(L^p\)-regularity\(H^{\infty}\)-functional calculushydrostatic Stokes operator

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) One-parameter semigroups and linear evolution equations (47D06) Stokes and related (Oseen, etc.) flows (76D07) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items (10)

Global wellposedness of the primitive equations with nonlinear equation of state in critical spaces ⋮ The hydrostatic Stokes semigroup and well-posedness of the primitive equations on spaces of bounded functions ⋮ The primitive equations with stochastic wind driven boundary conditions ⋮ Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier–Stokes equations* ⋮ A remark for spatial analyticity around straining flows ⋮ Analysis of Viscous Fluid Flows: An Approach by Evolution Equations ⋮ Primitive equations with horizontal viscosity: the initial value and the time-periodic problem for physical boundary conditions ⋮ Well-posedness of the 3D stochastic primitive equations with multiplicative and transport noise ⋮ The hydrostatic approximation for the primitive equations by the scaled Navier-Stokes equations under the no-slip boundary condition ⋮ The primitive equations in the scaling-invariant space \(L^{\infty}(L^1)\)

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