Universality classes in Burgers turbulence

Details Universality classes in Burgers turbulence Universality classes in Burgers turbulence

2006-07-06

arxiv.org/abs/nlin/0607007v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

Scientific paper

10.1007/s00220-007-0251-1

We establish necessary and sufficient conditions for the shock statistics to approach self-similar form in Burgers turbulence with L\'{e}vy 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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