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}
}
  • C. Cao, E. Titi
  • Published 25 October 2010
  • Mathematics
  • Communications in Mathematical Physics
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… 
Global Well-posedness of the 3D Primitive Equations with Only Horizontal Viscosity and Diffusion
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
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
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 primitive equations approximation of the anisotropic horizontally viscous 3D Navier-Stokes equations
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
Rigorous derivation of the primitive equations with full viscosity and full diffusion 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 balance. On
Local and Global Well-Posedness of Strong Solutions to the 3D Primitive Equations with Vertical Eddy Diffusivity
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.
An Approach to the Primitive Equations for Oceanic and Atmospheric Dynamics by Evolution Equations
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
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 53 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
GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO
Models with a vanishing anisotropic viscosity in the vertical direction are of relevance for the study of turbulent flows in geophysics. This motivates us to study the two-dimensional Boussinesq
A Simple Friction and Diffusion Scheme for Planetary Geostrophic Basin Models
A simple friction and diffusion scheme is proposed for use with the time-dependent planetary geostrophic equations, which in their proper asymptotic form cannot be solved in a closed basin. The
GLOBAL WELL-POSEDNESS OF THE VISCOUS BOUSSINESQ EQUATIONS
We prove the global well-posedness of the viscous incompressible Boussinesq equations in two spatial dimensions for general initial data in $H^m$ with $m\ge 3$. It is known that when both the
Small‐scale structures in Boussinesq convection
Two‐dimensional Boussinesq convection is studied numerically using two different methods: a filtered pseudospectral method and a high‐order accurate eno scheme. The issue whether finite time
Global regularity for the 2D Boussinesq equations with partial viscosity terms
Global well‐posedness and finite‐dimensional global attractor for a 3‐D planetary geostrophic viscous model
In this paper we consider a three‐dimensional planetary geostrophic viscous model of the gyre‐scale mid‐latitude ocean. We show the global existence and uniqueness of the weak and strong solutions to
On the regularity of the primitive equations of the ocean
We prove the existence of global strong solutions of the primitive equations of the ocean in the case of the Dirichlet boundary conditions on the side and the bottom boundaries including the varying
Vorticity and incompressible flow
Preface 1. An introduction to vortex dynamics for incompressible fluid flows 2. The vorticity-stream formulation of the Euler and the Navier-Stokes equations 3. Energy methods for the Euler and the
Navier-Stokes equations
A criterion is given for the convergence of numerical solutions of the Navier-Stokes equations in two dimensions under steady conditions. The criterion applies to all cases, of steady viscous flow in
...
1
2
3
4
5
...