• DOI:10.4007/ANNALS.2007.166.245
• Corpus ID: 12690494

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 effects under the Boussinesq approximation. Moreover, and due to the shallowness of the oceans and the atmosphere, i.e., the depth of the fluid layer is very small in comparison to the radius of the earth, the vertical large scale motion in the oceans and the atmosphere is much smaller than the horizontal one, which in turn leads to modeling the vertical motion by the hydrostatic balance. As a result