• C. GIRAUD

Code(s) de Classification MSC:

• 35Q53 KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.), See also {58F07}
• 60H15 Stochastic partial differential equations, See also {35R60}
• 60J65 Brownian motion, See also {58G32}

Résumé: We study the set of regular points (i.e. the points which have not been involved into shocks up to time $t$) for the inviscid Burgers equation in dimension 1 when initial velocity is a stable Lévy noise. We prove first that when the noise is not completely asymmetric and has index $\A \in (1/2,1)$, the set of regular points is discrete a.s. and regenerative. Then, we show that in the case of the Cauchy noise, the set of regular points is uncountable, with Minkowsky dimension 0.

Mots Clés: Burgers turbulence ; stable Lévy noise ; regular points

Date: 2000-02-21

Prépublication numéro: PMA-569

Postcript file : PMA-569.ps