Statistics of shocks in solutions of inviscid Burgers equation

Ya G. Sinai

Research output: Contribution to journalArticlepeer-review

181 Scopus citations


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
Issue number3
StatePublished - Sep 1992

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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