Space-time stationary solutions of Burgers equation with random forcing

Thursday, October 25, 2012 - 3:15pm - 4:05pm
Keller 3-180
Yuri Bakhtin (Georgia Institute of Technology)
The Burgers equation is a basic hydrodynamic model
describing the evolution of the velocity field of sticky dust
particles. When supplied with random forcing it turns into an
infinite-dimensional random dynamical system that has been studied
since late 1990's. The variational approach to Burgers equation allows
to study the system by analyzing optimal paths in the random landscape
generated by the random force potential. Therefore, this is
essentially a random media problem. For a long time only compact cases
of Burgers dynamics on the circle or a torus were understood well. In
this talk I discuss the Burgers dynamics on the entire real line with
no compactness or periodicity assumption. The main result is the
description of the ergodic components and One Force One Solution
principle on each component. Joint work with Eric Cator and Kostya
MSC Code: