Burgers turbulence and random Lagrangian systems

R. Iturriaga, K. Khanin

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)


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 languageEnglish
Pages (from-to)377-428
Number of pages52
JournalCommunications in Mathematical Physics
Issue number3
Publication statusPublished - Jan 2003


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