Videos

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

Presenter
February 25, 2010
Keywords:
  • Navier-Stokes equations
MSC:
  • 35Q30
Abstract
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.