Universality classes in Burgers turbulence

Abstract

We establish necessary and sufficient conditions for the shock statistics to approach self-similar form in Burgers turbulence with Lévy 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.

References in corpus (2)

• Markovian solutions of inviscid Burgers equation
• Some aspects of additive coalescents

Cited by in corpus (12)

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• An invariant in shock clustering and Burgers turbulence
• Conservation Laws With Random and Deterministic Data
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• Coarse graining, dynamic renormalization and the kinetic theory of shock clustering