# Global Well–Posedness of the 3D Primitive Equations with Partial Vertical Turbulence Mixing Heat Diffusion

@article{Cao2010GlobalWO, title={Global Well–Posedness of the 3D Primitive Equations with Partial Vertical Turbulence Mixing Heat Diffusion}, author={Chongsheng Cao and Edriss S. Titi}, journal={Communications in Mathematical Physics}, year={2010}, volume={310}, pages={537-568} }

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 called the primitive equations. To overcome the turbulence mixing a partial vertical diffusion is usually added to the temperature advection (or density stratification) equation. In this paper we prove the global regularity of strong solutions to this model in a three-dimensional infinite horizontal…

## 54 Citations

Global Well-posedness of the 3D Primitive Equations with Only Horizontal Viscosity and Diffusion

- Mathematics
- 2014

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…

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

- Mathematics
- 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 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…

Global strong Lp well-posedness of the 3D primitive equations with heat and salinity diffusion

- Mathematics
- 2016

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

- MathematicsJournal of Differential Equations
- 2022

Finite-Time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric Dynamics

- Mathematics
- 2012

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…

Rigorous derivation of the primitive equations with full viscosity and full diffusion 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 balance. On…

Local and Global Well-Posedness of Strong Solutions to the 3D Primitive Equations with Vertical Eddy Diffusivity

- Mathematics
- 2014

In this paper, we consider the initial-boundary value problem of the viscous 3D primitive equations for oceanic and atmospheric dynamics with only vertical diffusion in the temperature equation.…

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

- Mathematics
- 2017

An Approach to the Primitive Equations for Oceanic and Atmospheric Dynamics by Evolution Equations

- Mathematics
- 2020

The primitive equations for oceanic and atmospheric dynamics are a fundamental model for many geophysical flows. In this chapter we present a summary of an approach to these equations based on the…

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