The primitive equations as the small aspect ratio limit of the Navier-Stokes equations: rigorous justification of the hydrostatic approximation

DOI10.1016/j.matpur.2018.04.006zbMath1412.35224arXiv1706.08885OpenAlexW2963344559WikidataQ129963580 ScholiaQ129963580MaRDI QIDQ1732991

Edriss S. Titi, Jinkai Li

Publication date: 26 March 2019

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.08885

zbMATH Keywords

primitive equationsanisotropic Navier-Stokes equationshydrostatic approximation (balance)small aspect ratio limit

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Hydrology, hydrography, oceanography (86A05) Navier-Stokes equations (35Q30) Meteorology and atmospheric physics (86A10) PDEs in connection with geophysics (35Q86)

Related Items (30)

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Cites Work

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• Global well-posedness of strong solutions to a tropical climate model
• Global strong \(L^{p}\) well-posedness of the 3D primitive equations with heat and salinity diffusion
• Strong solutions to the 3D primitive equations with only horizontal dissipation: near \(H^{1}\) initial data
• Local and global well-posedness of strong solutions to the 3D primitive equations with vertical Eddy diffusivity
• Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity
• Global well-posedness of the \(3D\) primitive equations with partial vertical turbulence mixing heat diffusion
• On the uniqueness of \(z\)-weak solutions of the three-dimensional primitive equations of the ocean
• On the uniqueness of weak solutions of the two-dimensional primitive equations.
• Mathematical theory for the coupled atmosphere-ocean models (CAO III)
• Finite-time blowup for the inviscid primitive equations of oceanic and atmospheric dynamics
• The regularity of solutions of the primitive equations of the ocean in space dimension three
• Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics
• Existence of a solution `in the large' for the 3D large-scale ocean dynamics equations
• Global strong well-posedness of the three dimensional primitive equations in \({L^p}\)-spaces
• Mathematical Justification of the Hydrostatic Approximation in the Primitive Equations of Geophysical Fluid Dynamics
• A tropical atmosphere model with moisture: global well-posedness and relaxation limit
• Stability of Two-Dimensional Viscous Incompressible Flows under Three-Dimensional Perturbations and Inviscid Symmetry Breaking
• Existence and Uniqueness of Weak Solutions to Viscous Primitive Equations for a Certain Class of Discontinuous Initial Data
• 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
• A Vertical Diffusion Model for Lakes
• Global well‐posedness and finite‐dimensional global attractor for a 3‐D planetary geostrophic viscous model
• Primitive equations with continuous initial data
• On the regularity of the primitive equations of the ocean
• Blowup of solutions of the hydrostatic Euler equations
• Sobolev and Gevrey regularity results for the primitive equations in three space dimensions

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