# Strong solutions to the 3D primitive equations with only horizontal dissipation: near $H^1$ initial data

@article{Cao2016StrongST, title={Strong solutions to the 3D primitive equations with only horizontal dissipation: near \$H^1\$ initial data}, author={Chongsheng Cao and Jinkai Li and Edriss S. Titi}, journal={arXiv: Analysis of PDEs}, year={2016} }

## 40 Citations

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

- Mathematics
- 2017

Primitive equations with horizontal viscosity: The initial value and The time-periodic problem for physical boundary conditions

- Mathematics
- 2019

The $3D$-primitive equations with only horizontal viscosity are considered on a cylindrical domain $(-h,h)\times G$, $G\subset \mathbb{R}^2$ smooth, with the physical Dirichlet boundary conditions on…

A Tropical Atmosphere Model with Moisture: Global Well-posedness and Relaxation Limit

- Mathematics
- 2015

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.;…

Global well-posedness of strong solutions to a tropical climate model

- Mathematics
- 2015

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 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…

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 Well-Posedness of Reduced 3D Primitive Geostrophic Adjustment Model with Weak Dissipation

- Mathematics
- 2019

Author(s): Cao, Chongsheng; Lin, Quyuan; Titi, Edriss S | Abstract: In this paper we prove the local well-posedness and global well-posedness with small initial data of the strong solution to the…

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…

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

- MathematicsJournal of Differential Equations
- 2022

## References

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

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

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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

- Mathematics
- 2015

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.;…

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 well-posedness of strong solutions to a tropical climate model

- Mathematics
- 2015

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

- Mathematics
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Existence of a Solution “in the Large” for Ocean Dynamics Equations

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Abstract.For the system of equations describing the large-scale ocean dynamics, an existence and uniqueness theorem is proved “in the large”. This system is obtained from the 3D Navier–Stokes…

Existence and Uniqueness of Weak Solutions to Viscous Primitive Equations for a Certain Class of Discontinuous Initial Data

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This work proves the global existence and uniqueness of weak solutions, with the initial data taken as small $L^\infty$ perturbations of functions in the space X, by generalizing in a uniform way the result on the uniqueness of strong solutions with continuous initial data.

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…