Speaker

:

Dr. Gautam Iyer

Subject Area

:

Mathematics

Venue

:

Lecture Hall - I, Dept of Mathematics

Time

:

2.30 pm

Date  

:

Jan 2,2009 (Friday)

Title

:

Stochastic Lagrangian Particle systems for the Navier-Stokes and Burgers equations

I will introduce an exact stochastic representation for certain non-linear transport equations (e.g. 3D-Navier-Stokes, Burgers)   based on noisy Lagrangian paths, and use this to construct a   (stochastic) particle system for the Navier-Stokes equations. On any   fixed time interval, this particle system converges to the   Navier-Stokes equations as the number of particles goes to infinity.

Curiously, a similar system for the (viscous) Burgers equations   shocks almost surely in finite time. This happens because these   particle systems exhibit a curious energy dissipation on long time intervals. I will describe a resetting procedure by which these shocks can (surprisingly!) be avoided, and thus obtain convergence
to the viscous Burgers equations on long time intervals