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}
}
The hydrostatic approximation of the Boussinesq equations with rotation in a thin domain
Abstract. In this paper, we improve the global existence result in [9] slightly. More precisely, the global existence of strong solutions to the primitive equations with only horizontal viscosity and
On the rigorous mathematical derivation for the viscous primitive equations with density stratification
In this paper, we rigorously derive the governed equations describing the motion of stable stratified fluid, from the mathematical point of view. Specially, we prove that the scaled Boussinesq
Rigorous derivation of the full primitive equations by scaled Boussinesq equations
The primitive equations of large-scale ocean dynamics form the fundamental model in geophysical flows. It is well-known that the primitive equations can be formally derived by hydrostatic
On the effect of fast rotation and vertical viscosity on the lifespan of the $3D$ primitive equations
We study the effect of the fast rotation and vertical viscosity on the lifespan of solutions to the three-dimensional primitive equations (also known as the hydrostatic Navier-Stokes equations) with
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

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In this paper, we consider the initial boundary value problem of the three‐dimensional primitive equations for planetary oceanic and atmospheric dynamics with only horizontal eddy viscosity in the
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
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