| Date: Monday, April 18, 2011
Title: On the Question of Global Regularity for Three-dimensional Navier-Stokes
Equations and Relevant Geophysical Models
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. Inspired by this work I will also provide a new global regularity criterion for the three-dimensional Navier-Stokes equations involving the pressure. This is joint work with Chongsheng Cao.
Speaker: Edriss Titi
Institution: Weizmann Institute, Israel, and University of California, Irvine
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