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

@article{Cao2005GlobalWO,
  title={Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics},
  author={Chongsheng Cao and Edriss S. Titi},
  journal={Annals of Mathematics},
  year={2005},
  volume={166},
  pages={245-267}
}
  • C. Cao, E. Titi
  • Published 2 March 2005
  • Mathematics, Environmental Science
  • Annals of Mathematics
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 dynamics. 1. Introduction Large scale dynamics of oceans and atmosphere is governed by the primitive equations which are derived from the Navier-Stokes equations, with rotation, coupled to thermodynamics and salinity diffusion-transport equations, which account for the buoyancy forces and stratification… 

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References

SHOWING 1-10 OF 41 REFERENCES

Large-scale circulation with small diapycnal diffusion: The two-thermocline limit

The structure and dynamics of the large-scale circulation of a single-hemisphere, closed-basin ocean with small diapycnal diffusion are studied by numerical and analytical methods. The investigation

On the equations of the large-scale ocean

As a preliminary step towards understanding the dynamics of the ocean and the impact of the ocean on the global climate system and weather prediction, the authors study the mathematical formulations

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

Some mathematical properties of the planetary geostrophic equations for large-scale ocean circulation

We study in this article the well-posdness of the planetary geostrophic equations of the gyre-scale midlatitude ocean, and address in particular the question of the existence and some properties of

An intermediate model for large-scale ocean circulation studies

A ‘horizontal’ hyper-diffusion three-dimensional thermocline planetary geostrophic model: well-posedness and long-time behaviour

In this paper, we study a three-dimensional thermocline planetary geostrophic 'horizontal' hyper-diffusion model of the gyre-scale midlatitude ocean. We show the global existence and uniqueness of

The primitive equations on the large scale ocean under the small depth hypothesis

In this article we study the global existence of strong solutions of the Primitive Equations (PEs) for the large scale ocean under the small depth hypothesis. The small depth hypothesis implies

The Use of the Primitive Equations of Motion in Numerical Prediction

An obstacle to the use of the primitive hydrodynamical equations for numerical prediction is that the initial wind and pressure fields determined by conventional means give rise to spurious

FAST SINGULAR OSCILLATING LIMITS AND GLOBAL REGULARITY FOR THE 3D PRIMITIVE EQUATIONS OF GEOPHYSICS

Fast singular oscillating limits of the three-dimensional "primitive" equations of geophysical fluid flows are analyzed. We prove existence on infinite time intervals of regular solutions to the 3D

New formulations of the primitive equations of atmosphere and applications

The primitive equations are the fundamental equations of atmospheric dynamics. With the purpose of understanding the mechanism of long-term weather prediction and climate changes, the authors study