Jin Feng
University of Kansas
Title: Large time coherent structure for a 2-D vortex flow model
The vorticity formulation of 2-D incompressible Navier-Stokes equation can be viewed as mean-field limit of stochastic interacting point vortices. In such model context, the action functional for probabilistic large deviation principle (large particle number limit) characterizes Boltzmann entropy for the stochastic system in path space, in any finite time. It characterizes fluctuation around incompressible Euler equation. We then study a large time and inviscid limit of such functional as a variational/optimal control problem in space of measures. The whole program rigorously justify the Onsager-Joyce-Montgomery theory starting from a non-equilibrium level. We will use the tools of large deviation, Hamilton-Jacobi equation in space of measures and optimal mass transportation theory to explain the procedure.
©2010, Department of Mathematical Sciences
Last Modified: February 26, 2009