The basic problem faced in geophysical fluid dynamics is that a mathematical description based only on fundamental physical principles, which are called the ``Primitive Equations'', is often prohibitively expensive computationally, and hard to study analytically. In this talk we 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 than thethree-dimensional Navier--Stokes equations we will show in this talk that they have globally (in time) unique regular solution for all initial data. This is a joint work with Chongshen Cao.

Lecture #12195

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