The primitive equations approximation of the anisotropic horizontally viscous 3D Navier-Stokes equations

@article{Li2022ThePE,
  title={The primitive equations approximation of the anisotropic horizontally viscous 3D Navier-Stokes equations},
  author={Jinkai Li and Edriss S. Titi and Guo Yuan},
  journal={Journal of Differential Equations},
  year={2022}
}
2 Citations
Global well-posedness of $z$-weak solutions to the primitive equations without vertical diffusivity
In this paper, we consider the initial boundary value problem in a cylindrical domain to the three dimensional primitive equations with full eddy viscosity in the momentum equations but with only
Local Martingale Solutions and Pathwise Uniqueness for the Three-dimensional Stochastic Inviscid Primitive Equations
We study the stochastic effect on the three-dimensional inviscid primitive equations (PEs, also called the hydrostatic Euler equations). Specifically, we consider a larger class of noises than

References

SHOWING 1-10 OF 63 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
The primitive equations as the small aspect ratio limit of the Navier–Stokes equations: Rigorous justification of the hydrostatic approximation
  • Jinkai Li, E. Titi
  • Mathematics, Physics
    Journal de Mathématiques Pures et Appliquées
  • 2019
An important feature of the planetary oceanic dynamics is that the aspect ratio (the ratio of the depth to horizontal width) is very small. As a result, the hydrostatic approximation (balance),
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 Three-Dimensional Primitive Equations with Only Horizontal Viscosity and Diffusion
© 2015 Wiley Periodicals, Inc. In this paper, we consider the initial boundary value problem of the three-dimen-sional primitive equations for planetary oceanic and atmospheric dynamics with only
Global existence of weak solutions to 3D compressible primitive equations with degenerate viscosity
In this paper, we investigate the compressible primitive equations (CPEs) with density-dependent viscosity for large initial data. The CPE model can be derived from the 3D compressible and
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.
The hydrostatic approximation for the primitive equations by the scaled Navier–Stokes equations under the no-slip boundary condition
In this paper we justify the hydrostatic approximation of the primitive equations in the maximal $L^p$-$L^q$-setting in the three-dimensional layer domain $\Omega = \Torus^2 \times (-1, 1)$ under the
Strong solutions to the 3D primitive equations with only horizontal dissipation: near $H^1$ initial data
In this paper, we consider the initial-boundary value problem of the three-dimensional primitive equations for oceanic and atmospheric dynamics with only horizontal viscosity and horizontal
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