Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier–Stokes equations*

DOI10.1088/1361-6544/aba509zbMath1452.35150arXiv1808.02410OpenAlexW2887357036MaRDI QIDQ5136535

Amru Hussein, Matthias Hieber, Marc Wrona, Takahito Kashiwabara, Ken Furukawa, Yoshikazu Giga

Publication date: 26 November 2020

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.02410

zbMATH Keywords

strong convergenceconvergence rateprimitive equationsscaled Navier-Stokes equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) One-parameter semigroups and linear evolution equations (47D06) Meteorology and atmospheric physics (86A10) PDEs in connection with geophysics (35Q86)

Related Items (12)

Global well-posedness of z-weak solutions to the primitive equations without vertical diffusivity ⋮ On the hydrostatic approximation of compressible anisotropic Navier-Stokes equations-rigorous justification ⋮ The primitive equations approximation of the anisotropic horizontally viscous \(3D\) Navier-Stokes equations ⋮ Higher-order error estimates for physics-informed neural networks approximating the primitive equations ⋮ On the rigorous mathematical derivation for the viscous primitive equations with density stratification ⋮ Global existence and asymptotic stability of the free boundary problem of the primitive equations with heat insulation ⋮ Blow-up criterion of solutions of the horizontal viscous primitive equations with horizontal eddy diffusivity ⋮ Rigorous derivation of the full primitive equations by the scaled Boussinesq equations with rotation ⋮ Analysis of Viscous Fluid Flows: An Approach by Evolution Equations ⋮ On the hydrostatic approximation of compressible anisotropic Navier-Stokes equations ⋮ Preface ⋮ The hydrostatic approximation for the primitive equations by the scaled Navier-Stokes equations under the no-slip boundary condition

Cites Work

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• Global Well-Posedness of the Three-Dimensional Primitive Equations with Only Horizontal Viscosity and Diffusion
• New formulations of the primitive equations of atmosphere and applications
• On the equations of the large-scale ocean
• Some estimates for the anisotropic Navier-Stokes equations and for the hydrostatic approximation
• Analyticity of solutions to the primitive equations
• Bounded 𝐻^{∞}-calculus for the hydrostatic Stokes operator on 𝐿^{𝑝}-spaces and applications

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