Burgers equation with random forcing

Stochastics Seminar
Thursday, February 26, 2015 - 15:05
1 hour (actually 50 minutes)
Skiles 006
Courant Institute of Mathematical Sciences, New York University
Ergodic theory of randomly forced space-time homogeneous Burgers equation in noncompact setting has been developed in a recent paper by Eric Cator , Kostya Khanin, and myself. The analysis is based on first passage percolation methods that allow to study coalescing one-sided action minimizers and construct the global solution via Busemann functions. i will talk about this theory and its extension to the case of space-continuous kick forcing. In this setting, the minimizers do not coalesce, so for the ergodic program to go through, one must use new soft results on their behavior to define generalized Busemann functions along appropriate subsequences.