We consider a spatially periodic inviscid random forced Burgers equation in arbitrary dimension and the random time-dependent Lagrangian system related to it. We construct a unique stationary distribution for "viscosity" solutions of the Burgers equation. We also show that with probability 1 there exists a unique minimizing trajectory for the random Lagrangian system which generates a non-trivial ergodic invariant measure for the non-random skew-product extension of the Lagrangian system.
|Number of pages||52|
|Journal||Communications in Mathematical Physics|
|Publication status||Published - Jan 2003|