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Communications in Mathematical Physics

, Volume 203, Issue 3, pp 729–741 | Cite as

Structure of Shocks in Burgers Turbulence¶with Stable Noise Initial Data

  • Jean Bertoin

Abstract:

Burgers equation can be used as a simplified model for hydrodynamic turbulence. The purpose of this paper is to study the structure of the shocks for the inviscid equation in dimension 1 when the initial velocity is given by a stable Lévy noise with index α∈ (1/2,2]. We prove that Lagrangian regular points exist (i.e. there are fluid particles that have not participated in shocks at any time between 0 and t) if and only if α≤ 1 and the noise is not completely asymmetric, and that otherwise the shock structure is discrete. Moreover, in the Cauchy case α= 1, we show that there are no rarefaction intervals, i.e. at time t >0$, there are fluid particles in any non-empty open interval.

Keywords

Initial Data Initial Velocity Open Interval Burger Equation Regular Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Jean Bertoin
    • 1
  1. 1.Laboratoire de Probabilités, Université Pierre et Marie Curie, 4, Place Jussieu, F-75252 Paris Cedex 05, France. E-mail: jbe@ccr.jussieu.frFR

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