##### Department of Mathematics,

University of California San Diego

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### Analysis Seminar

## Edriss Titti

#### UC Irvine

## On the Question of Global Regularity for Three-dimensional Navier-Stokes Equations and Relevant Geophysical Models

##### Abstract:

\noindent 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. \vskip .2in \noindent Inspired by this work I will also provide a new global regularity criterion for the three-dimensional Navier-Stokes equations involving the pressure. \vskip .2in \noindent This is a joint work with Chongsheng Cao.

Host: Hans Lindblad

### February 2, 2010

### 10:00 AM

### AP&M 7321

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