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.
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Received: 25 March 2002 / Accepted: 30 July 2002 Published online: 22 November 2002
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Iturriaga, R., Khanin, K. Burgers Turbulence and Random Lagrangian Systems. Commun. Math. Phys. 232, 377–428 (2003). https://doi.org/10.1007/s00220-002-0748-6
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DOI: https://doi.org/10.1007/s00220-002-0748-6