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Stochastic particle methods for the Navier-Stokes and Burgers equations
PDE & Applied Mathematics| Speaker: | Gautam Iyer, Stanford |
| Location: | 1147 MSB |
| Start time: | Wed, Jun 3 2009, 11:10AM |
Description
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.
Note special time.