# 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} }

## 6 Citations

The hydrostatic approximation of the Boussinesq equations with rotation in a thin domain

- Mathematics
- 2022

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

- Mathematics
- 2022

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

- Mathematics
- 2021

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

- Mathematics
- 2022

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

- MathematicsJournal of Mathematical Physics
- 2022

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

- Mathematics
- 2022

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

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Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics

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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

- MathematicsJournal de Mathématiques Pures et Appliquées
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Global Well–Posedness of the 3D Primitive Equations with Partial Vertical Turbulence Mixing Heat Diffusion

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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

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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 existence of weak solutions to 3D compressible primitive equations with degenerate viscosity

- Mathematics
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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…

Global Well-Posedness of the Three-Dimensional Primitive Equations with Only Horizontal Viscosity and Diffusion

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- 2016

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…

Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity

- Mathematics
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Mathematical Justification of the Hydrostatic Approximation in the Primitive Equations of Geophysical Fluid Dynamics

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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

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- 2020

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…