Abstract
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.
| Original language | English |
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| Pages (from-to) | 377-428 |
| Number of pages | 52 |
| Journal | Communications in Mathematical Physics |
| Volume | 232 |
| Issue number | 3 |
| Publication status | Published - Jan 2003 |