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

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

On regular points in Burgers turbulence with stable noise initial data


Code(s) de Classification MSC:

RÚsumÚ: 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 LÚvy 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 ClÚs: Burgers turbulence ; stable LÚvy noise ; regular points

Date: 2000-02-21

Prépublication numéro: PMA-569

Postcript file : PMA-569.ps