##### Department of Mathematics,

University of California San Diego

****************************

### Math 295 - Mathematics Colloquium

## Vladimir Sverak

#### University of Minnesota

## PDE aspects of Navier-Stokes Equations

##### Abstract:

Solutions of incompressible Navier-Stokes equations can exhibit a wide spectrum of different types of behavior. In various regimes, the equations contain as special limiting cases for example the classical heat equation, the non-linear Schroedinger equation, various other dispersive equations with strange dispersion relations, various non-trivial finite-dimensional dynamical systems, some classical geometric semilinear elliptic equations, etc. In addition, when thinking about realistic fluid flows and applications, ideas from statistical mechanics enter the picture. In the lecture I will explain (a limited number of) some PDE aspects of these equations.

Host: Ruth Williams

### April 5, 2007

### 4:00 PM

### AP&M 6402

****************************