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

@article{Li2019ThePE,
  title={The primitive equations as the small aspect ratio limit of the Navier–Stokes equations: Rigorous justification of the hydrostatic approximation},
  author={Jinkai Li and Edriss S. Titi},
  journal={Journal de Math{\'e}matiques Pures et Appliqu{\'e}es},
  year={2019}
}
  • Jinkai Li, E. Titi
  • Published 26 June 2017
  • Mathematics
  • Journal de Mathématiques Pures et Appliquées
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Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier–Stokes equations
Consider the anisotropic Navier-Stokes equations as well as the primitive equations. It is shown that the horizontal velocity of the solution to the anisotropic Navier-Stokes equations in a
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References

SHOWING 1-10 OF 54 REFERENCES
Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics
In this paper we prove the global existence and uniqueness (regularity) of strong solutions to the three-dimensional viscous primitive equations, which model large scale ocean and atmosphere
Mathematical Justification of the Hydrostatic Approximation in the Primitive Equations of Geophysical Fluid Dynamics
TLDR
A convergence and existence theorem is proved for this asymptotic model of the time-dependent incompressible Navier-Stokes equations by means of anisotropic estimates and a new time-compactness criterium.
Recent Advances Concerning Certain Class of Geophysical Flows
Author(s): Li, Jinkai; Titi, Edriss S | Abstract: This paper is devoted to reviewing several recent developments concerning certain class of geophysical models, including the primitive equations
On the equations of the large-scale ocean
As a preliminary step towards understanding the dynamics of the ocean and the impact of the ocean on the global climate system and weather prediction, the authors study the mathematical formulations
Global well-posedness of strong solutions to a tropical climate model
In this paper, we consider the Cauchy problem to the TROPIC CLIMATE MODEL derived by Frierson-Majda-Pauluis in [Comm. Math. Sci, Vol. 2 (2004)] which is a coupled system of the barotropic and the
Global Well–Posedness of the 3D Primitive Equations with Partial Vertical Turbulence Mixing Heat Diffusion
The three–dimensional incompressible viscous Boussinesq equations, under the assumption of hydrostatic balance, govern the large scale dynamics of atmospheric and oceanic motion, and are commonly
Finite-Time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric Dynamics
In an earlier work we have shown the global (for all initial data and all time) well-posedness of strong solutions to the three-dimensional viscous primitive equations of large scale oceanic and
Global Well-posedness of the 3D Primitive Equations with Only Horizontal Viscosity and Diffusion
In this paper, we consider the initial-boundary value problem of the 3D primitive equations for planetary oceanic and atmospheric dynamics with only horizontal eddy viscosity in the horizontal
A Tropical Atmosphere Model with Moisture: Global Well-posedness and Relaxation Limit
In this paper, we consider a nonlinear interaction system between the barotropic mode and the first baroclinic mode of the tropical atmosphere with moisture; that was derived in [Frierson, D.M.W.;
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