The basic problem faced in geophysical fluid dynamics is that a mathematical description based only
on fundamental physical principles, the so-called the “Primitive Equations”, is often prohibitively
expensive computationally, and hard to study analytically. In this talk I will survey the main
obstacles in proving the global regularity for the three-dimensional Navier–Stokes equations and
their geophysical counterparts. Even though the Primitive Equations look as if they are more
difficult to study analytically than the three-dimensional Navier–Stokes equations I will show in
this talk that they have a unique global (in time) regular solution for all initial data.
This is a joint work with Chongshen Cao.