Randomly forced CGL equation: Stationary measures and the inviscid limit

Journal of Physics A: Mathematical and General

Volumn 37, Issue 12, 2004, Pages 3805-3822

  Kuksin, Sergei ^a,b   Shirikyan, Armen ^c  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

^b STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^c UNIVERSITÉ PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1842683021     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/12/006     Document Type: Article

References (28)

1. [BG80] Brézis H Gallouet T 1980 Nonlinear Schrödinger evolution equations Nonlinear Anal.4 677-81
2. [BGT03] Burq N, Gérard P and Tzvetkov N 2003 Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds Am. J. Math. at press
3. [BKL02] Bricmont J. Kupiainen A and Lefevere R 2002 Exponential mixing for the 2D stochastic Navier-Stokes dynamics Commun. Math. Phys. 230 87-132
4. [Bou99] Bourgain J 1999 Global Solutions of Nonlinear Schrödinger Equations (Providence, RI: American Mathematical Society)
5. [CK97] Chow P-L and Khasminskii R Z 1997 Stationary solutions of nonlinear stochastic evolution equations Stochastic Anal. Appl. 15 671-99
6. [DZ92] Da Prato G and Zabczyk J 1992 Stochastic Equations in Infinite Dimensions (Cambridge: Cambridge University Press)
7. [DZ96] Da Prato G and Zabczyk J 1996 Ergodicity for Infinite Dimensional Systems (Cambridge: Cambridge University Press)
8. [EMS01] E W, Mattingly J C and Sinai Ya G 2001 Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation Commun. Math. Phys. 224 83-106
9. [Hai02] Hairer M 2002 Exponential mixing properties of stochastic PDE's through asymptotic coupling Probab. Theory Relat. Fields 124 345-80
10. [KR77] Krylov N V and Rozovskiǐ B L 1977 The Cauchy problem for linear stochastic partial differential equations Math. USSR-Izv. 41 1267-84
11. [Kry95] Krylov N V 1995 Introduction to the Theory of Diffusion Processes (AMS Translations of Mathematical Monographs vol 142) (Providence, RI: American Mathematical Society)
12. p) spaces Electron. J. Probab. 5 29
13. [KS00] Kuksin S B and Shirikyan A 2000 Stochastic dissipative PDE's and Gibbs measures Commun. Math. Phys. 213 291-330
14. [KS01] Kuksin S B and Shirikyan A 2001 A coupling approach to randomly forced nonlinear PDE's: I Commun. Math. Phys. 221 351-66
15. [KS02] Kuksin S B and Shirikyan A 2002 Coupling approach to white-forced nonlinear PDE's J. Math. Pures Appl. 81 567-602
16. [Kuk99] Kuksin S B 1999 A stochastic nonlinear Schrödinger equation: I. A priori estimates Tr. Mat. Inst. Steklova 225 232-56
17. [Kuk00] Kuksin S B 2000 Analysis of Hamiltonian PDEs (Oxford: Oxford University Press)
18. [Kuk03] Kuksin S B 2004 The Eulerian limit for 2D statistical hydrodynamics J. Stat. Phys. 35 1250-1310
19. [Lio69] Lions J-L 1969 Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires (Paris: Gauthier-Villars)
20. [Mat02] Mattingly J 2002 Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics Commun. Math. Phys 230 421-62
21. p-theory for systems of SPDEs Electron. J. Probab. 6 35
22. [MR03] Mikulevicius R and Rozovskii B 2003 Stochastic Navier-Stokes equations for turbulent flows SIAM J. Math. Anal. 35 1250-1310
23. [Par79] Pardoux E 1979 Stochastic partial differential equations and filtering of diffusion processes Stochastics 3 127-67
24. [RS80] Reed M and Simon B 1980 Methods of Modern Mathematical Physics: I. Functional Analysis (New York: Academic)
25. [Shi02] Shirikyan A 2002 Analyticity of solutions for randomly forced two-dimensional Navier-Stokes equations Russ. Math. Surv. 57 785-99
26. [Shi03] Shirikyan A 2003 Exponential mixing for randomly forced PDEs: method of coupling (in preparation)
27. [SS99] Sulem C and Sulem P-L 1999 The Nonlinear Schrödinger Equation Applied Mathematical Sciences vol 139 (New York: Springer)
28. [VF88] Vishik M I and Fursikov A V 1988 Mathematical Problems in Statistical Hydromechanics (Dordrecht: Kluwer)