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Stochastic particle methods for the Navier-Stokes and Burgers equations

PDE and Applied Math Seminar

Speaker: Gautam Iyer, Stanford
Location: 1147 MSB
Start time: Wed, Jun 3 2009, 11:10AM

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.