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Publication 06-CNA-06

Universality Classes in Burgers Turbulence

Govind Menon
Division of Applied Mathematics
Brown University
Providence, RI 02912


Robert L. Pego
Department of Mathematical Sciences
Carnegie Mellon Univeristy
Pittsburgh, PA 15213

Abstract: We establish necessary and sufficient conditions for the shock statistics to approach self-similar form in Burgers turbulence with Levy process initial data. The proof relies upon an elegant closure theorem of Bertoin and Carraro and Duchon that reduces the study of shock statistics to Smoluchowski's coagulation equation with additive kernel, and upon our previous characterization of the domains of attraction of self-similar solutions for this equation.

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