Statistics and Data Science Seminar
Jin Feng
University of Kansas
From a stochastic vortex dynamic model to Onsager-Joyce-Montgomery theory
Abstract: The vorticity formulation of 2-D incompressible Navier-Stokes equation can be
viewed
as mean-field limit of stochastic interacting point vortices. As number of
particles goes
to infinity and viscosity term goes to zero, we arrive at inviscid limit of 2-D
incompressible
Euler equation.
We study multi-scale large deviation limits of such model, on the torus, as
particle number
and time go large but viscosity goes small. The result gives a first principle
approach to
establish the Onsager-Joyce-Montgomery theory as limit theorem derived from
microscopically
defined non-equilibrium models. The Onsager-Joyce-Montgomery theory concerns large
time coherent structures of vortex dynamics associated with 2-D Euler equation. It
was previously
informally formulated using equilibrium models only.
The talk is based on joint works (some of which are ongoing) of the speaker with
Fasto Gozzi,
Tom Kurtz and Andrzej Swiech, a SQuaRE team funded by American Institute of
Mathematics.
Wednesday April 25, 2012 at 4:00 PM in SEO 636