Probability and Math Finance Seminar
## Gautam Iyer, Department of Mathematical Sciences, Carnegie Mellon University

**A stochastic-Lagrangian approach to the Navier-Stokes equations**

**Abstract: **The Navier-Stokes equations are a system of (deterministic) PDE's which describe the evolution of the velocity field of a viscous (incompressible) fluid. I will begin by introducing these equations, and describing a method of `random characteristics' that can be used to provide an exact stochastic representation of solutions to these equations in the absence of spatial boundaries. The presence of spatial boundaries introduces certain technical difficulties, and I will indicate how these can be resolved.

I will finally talk a (probabilistic) global existence result motivated by the above framework which is related to the well known Clay institutes $1,000,000 millennium problem.

*MONDAY, November 30, 2009*

**Time:** 5:00 P.M.

**Location:** WeH 6423