Burgers equation with random forcing

Burgers equation with random forcing

-
Yuri Bakhtin , Courant Institute of Mathematical Sciences, New York University
Fine Hall 601

The Burgers equation is one of the basic nonlinear evolutionary PDEs. The study of ergodic properties of the Burgers equation with random forcing began in 1990's. The natural approach is based on the analysis of optimal paths in the random landscape generated by the random force potential. For a long time only compact cases of the Burgers dynamics on a circle or bounded interval were understood well. In this talk I will discuss the Burgers dynamics on the entire real line with no compactness or periodicity assumption on the random forcing. The main result is the description of the ergodic components and existence of a global attracting random solution in each component. The proof is based on ideas from the theory of first or last passage percolation. My new work on kicked forcing is an extension of joint work with Eric Cator and Kostya Khanin on Poissonian forcing.