Statistics of shocks in solutions of inviscid Burgers equation

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Abstract

The purpose of this paper is to analyze statistical properties of discontinuities of solutions of the inviscid Burgers equation having a typical realization b(y) of the Brownian motion as an initial datum. This case was proposed and studied numerically in the companion paper by She, Aurell and Frisch. The description of the statistics is given in terms of the behavior of the convex hull of the random process {Mathematical expression}. The Hausdorff dimension of the closed set of those y where the convex hull coincides with w is also studied.

Original languageEnglish (US)
Pages (from-to)601-621
Number of pages21
JournalCommunications in Mathematical Physics
Volume148
Issue number3
DOIs
StatePublished - Sep 1 1992

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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