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Burgers Turbulence and Dynamical Systems
Iturriaga, I.; Khanin, K.
Keyword(s): random burgers equation; random Hamilton-Jacobi equation; uniqueness of global minimizers
Abstract: We discuss a dynamical system approach to a problem of Burgers turbulence. It is shown that there exists a unique stationary distribution for solutions to spatially periodic inviscid random forced Burgers equation in arbitrary dimension. The construction is based on analysis of minimizing orbits for time- dependent random Lagrangians on a d-dimensional torus. We also discuss how dynamical properties of minimizing trajectories lead to quantitative predictions for physically important universal critical exponents. Notes: R. Iturriaga, Centro de Investigacion en Mathematica, Guanajuato, Mexico
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