Random Burgers equation and Lagrangian systems in non-compact domains

Nonlinearity

Volumn 16, Issue 3, 2003, Pages 819-842

  Hoang, Viet Ha ^a   Khanin, Konstantin ^b,c,d  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b ISAAC NEWTON INSTITUTE FOR MATHEMATICAL SCIENCES   (United Kingdom)

^c HERIOT WATT UNIVERSITY   (United Kingdom)

^d LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242287840     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/3/303     Document Type: Article

References (25)

1. Aubry S 992 The concept of anti-integrability: definition, theorems and applications to the standard map twist mappings and their applications IMA Vol. Math. Appl. 44 7-54
2. Balkovsky E, Falkovich G, Kolokolov I and Lebedev V 1997 Intermittency of Burgers turbulence Phys. Rev. Lett. 78 1452-5
3. Bec J 2001 Universality of velocity gradients in forced Burgers turbulence Phys. Rev. Lett. 87 104501
4. Bec J, Frisch U and Khanin K 2000 Kicked Burgers turbulence J. Fluid Mech. 416 239-67
5. Bec J, Iturriaga R and Khanin K 2002 Topological shocks in Burgers turbulence Phys. Rev. Lett. 89 024501
6. Bec J and Khanin K 2002 Forced Burgers equation in an unbounded domain J. Stat. Phys. submitted
7. Boldyrev S 1997 Velocity-difference probability density for Burgers turbulence Phys. Rev. E 55 6907-10
8. Bolotin S and MacKay R 1997 Multibump orbits near the anti-integrable limit for Lagrangian systems Nonlinearity 10 1015-29
9. Bouchaud J P, Mezard M and Parisi G 1995 Scaling and intermittency in Burgers turbulence Phys. Rev. E 52 3656-74
10. Chekhlov A and Yakhot V 1995 Kolmogorov turbulence in a random force-driven Burgers equation Phys. Rev. E 51 R2739-49
11. E W, Khanin K, Mazel A and Sinai Ya 2000 Invariant measures for Burgers equation with stochastic forcing Ann. Math. 151 877-960
12. E W, Khanin K, Mazel A and Sinai Ya 1997 Probability distribution functions for the random forced Burgers equations Phys. Rev. Lett. 78 1904-7
13. E W and Vanden Eijnden E 1999 Asymptotic theory for the probability density functions in Burgers turbulence Phys. Rev. Lea. 83 2572-5
14. E W and Vanden Eijnden E 2000 Statistical theory of the stochastic Burgers equation in the inviscid limit Comm. Pure Appl. Math. 53 852-901
15. Fathi A 2002 Weak KAM Theorem in Lagrangian Dynamics (Cambridge: Cambridge University Press)
16. Fathi A and Maderna E 2000 Weak KAM theorem on non-compact manifolds Preprint
17. Frisch U, Bec J and Villone B 2001 Singularities and the distribution of density in the Burgers/adhesion model Physica D 152/153 620-35
18. Gotoh T and Kraichnan R H 1998 Burgers turbulence with large scale forcing Phys. Fluids A 10 2859-66
19. Gurarie V and Migdal A 1996 Instantons in Burgers equations Phys. Rev. E 54 4908-14
20. Iturriaga R and Khanin K 2002 Burgers turbulence and random Lagrangian systems Commun. Math. Phys. at press
21. Kifer Yu 1997 The Burgers equation with a random force and a general model for directed polymers in random environments Prob. Theory Related Fields 108 29-65
22. Lax P D 1957 Hyperbolic systems of conservation laws Commun. Pure Appl. Math. 10 537-66
23. Lions P L 1982 Generalized Solutions of Hamilton-Jacobi Equations Research Notes in Math. vol 69 (Boston: Pitman Advanced Publishing Program)
24. Oleinik O A 1957 Discontinuous solutions of nonlinear differential equations Usp. Mat. Nauk 12 3-73
25. Polyakov A 1995 Turbulence without pressure Phys. Rev. E 52 6183-8