Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### On a Shock Front in Burgers Turbulence

Auteur(s):

Code(s) de Classification MSC:

• 35Q53 KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.), See also {58F07}
Résumé: We investigate how chaos propagates in the solution of Burgers equation $\partial_t u+u\,\partial_x u=0$ with initial condition $u(\cdot,0)$ distributed as a white noise on $\mathbb R^+$ and 0 on $\mathbb R^-$. We describe the evolution of the shock front that travels to the left. Asymptotics are given for both large and small time $t$.