Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**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