Statistics of shocks in solutions of inviscid Burgers equation

Ya G. Sinai

doi:10.1007/BF02096550

Statistics of shocks in solutions of inviscid Burgers equation

Ya G. Sinai

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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 language	English (US)
Pages (from-to)	601-621
Number of pages	21
Journal	Communications In Mathematical Physics
Volume	148
Issue number	3
DOIs	https://doi.org/10.1007/BF02096550
State	Published - Sep 1992

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02096550

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AB - 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.

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ER -

Statistics of shocks in solutions of inviscid Burgers equation

Abstract

All Science Journal Classification (ASJC) codes

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