Stochastic Lagrangian particle systems for the Navier-Stokes and<br/><br/> Burgers equations

Thursday, February 25, 2010 - 2:00pm - 2:45pm
EE/CS 3-180
Gautam Iyer (Stanford University)
Keywords: Navier Stokes, stochastic-Lagrangian, particle method.

Abstract: 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 in finite time, and solutions can not be continued past these
shocks using classical methods. 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.
MSC Code: