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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 28 September 1998 / Accepted: 12 January 1999
Rights and permissions
About this article
Cite this article
Bertoin, J. Structure of Shocks in Burgers Turbulence¶with Stable Noise Initial Data. Comm Math Phys 203, 729–741 (1999). https://doi.org/10.1007/s002200050633
Issue Date:
DOI: https://doi.org/10.1007/s002200050633