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Abstract: 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.
[LECTURE SLIDES]
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