Global Regularity for Three-dimensional Navier-Stokes Equations and Relevant Geophysical Models

PDE Seminar
Tuesday, April 26, 2011 - 11:00
1 hour (actually 50 minutes)
Skiles 005
UC Irvine and Wiezmann Institute
The basic problem faced in geophysical fluid dynamics isthat a mathematical description based only on fundamental physicalprinciples, the so-called the ``Primitive Equations'', is oftenprohibitively expensive computationally, and hard to studyanalytically. In this talk I will survey the main obstacles inproving the global regularity for the three-dimensionalNavier-Stokes equations and their geophysical counterparts. Eventhough the Primitive Equations look as if they are more difficult tostudy analytically than the three-dimensional Navier-Stokesequations 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 globalregularity criterion for the three-dimensional Navier-Stokesequations involving the pressure.This is a joint work with Chongsheng Cao.