Genealogy of shocks in Burgers turbulence with white noise initial velocity

被引：11

作者：

Giraud C. ^{[1
]}

机构：

[1] Lab. de Probabilites et Modeles A., Univ. Pierre et Marie Curie, C.N.R.S. UMR 7599, 75013 Paris, 175, rue du Chevaleret

来源：

Communications in Mathematical Physics | 2001年 / 223卷 / 1期

关键词：

White Noise; Initial Velocity; Time Pass; Fragmentation Process; Burger Equation;

D O I：

10.1007/s002200100528

中图分类号：

学科分类号：

摘要：

As time passes, the shocks of the solution of the inviscid Burgers equation aggregate. We characterize, in the case of white noise initial velocity, the stochastic fragmentation process obtained when time runs backwards. In other words, we specify the law of the genealogy of the shocks of the Burgers turbulence with white noise initial velocity.

引用

页码：67 / 86

页数：19

共 19 条

[1]

Abramowitz M., Stegun I.A., Handbook of Mathematical Functions, (1964)

[2]

Avellaneda M., Statistical properties of shocks in burgers turbulence, Commun. Math. Phys., 172, pp. 13-38, (1995)

[3]

Avellaneda M., Statistical properties of shocks in burgers turbulence II, Commun. Math. Phys., 169, pp. 45-59, (1995)

[4]

Bertoin J., The inviscid burgers equation with brownian initial velocity, Commun. Math. Phys., 193, pp. 397-406, (1998)

[5]

Bertoin J., Clustering statistics for sticky particles with Brownian initial velocity, J. Math. Pures Appl., 79, 2, pp. 173-194, (2000)

[6]

Burgers J.M., The Nonlinear Diffusion Equation, (1974)

[7]

Cole J.D., On a quasi linear parabolic equation occuring in aerodynamics, Quart. Appl. Math., 9, pp. 225-236, (1951)

[8]

Frachebourg L., Martin P.A., Exact statistical properties of the burgers equation, J. Fluids Mech.

[9]

Getoor R.K., Splitting times and shift functionals. Z. Wahrscheinlichkeitstheorie verw, Gebiete, 47, pp. 69-81, (1979)

[10]

Groeneboom P., The concave majorant of brownian motion, Ann. of Proba., 11, 4, pp. 1016-1027, (1983)

← 1 2 →