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

By Chongsheng Cao, Edriss S. Titi. 2005

469 citations recorded by the source corpus.

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

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/82afff1217ba124dee8309978fa09b5215c6c867

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Citations in the corpus

Regularity Criteria for the Three-dimensional Navier-Stokes Equations (2008, methodology): “We remark that a slightly weaker conditional regularity result for the 3D NSE which is involving conditions on one component of the pressure gradient, under different type of boundary conditions, has been reported in [9].”
Local martingale and pathwise solutions for an abstract fluids model (2010, background): “However to emphasize the notable differences between the stochastic Navier-Stokes Equations and the primitive equations we recall that the deterministic Primitive equations are known to be well posed in space dimension three (see [7, 27, 28]).”
Well-posedness of the hydrostatic Navier–Stokes equations (2018, background): “For positive values of tangential and transverse viscosity coefficients, they are known to be globally well-posed in the Sobolev setting in both the two and the three dimensional case [43, 3, 4, 40, 8, 21, 27, 28], and the vanishing viscosity limit η, η′ → 0 can be characterized in the real-analytic”
Some Mathematical Problems in Geophysical Fluid Dynamics (2009, methodology): “Recently, a series of three articles (Cao and Titi [2007], Kobelkov [2006], Kukavica and Ziane [2007a,b]) prove, by different methods, that the PEs have a 2D intrinsic structure and consequently prove the existence of global strong solutions. The first articles are those, written independently, by C”
Existence and Regularity of Invariant Measures for the Three Dimensional Stochastic Primitive Equations (2013, methodology): “The global existence of strong solutions was proven in [CT07], and later with a different approach in [Kob06], for the case of a cylindrical domain and Neumann boundary conditions on the top and the bottom of the ocean.”