Ergodicity for the stochastic complex Ginzburg-Landau equations
Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 4, p. 417-454
@article{AIHPB_2006__42_4_417_0,
     author = {Odasso, Cyril},
     title = {Ergodicity for the stochastic complex Ginzburg-Landau equations},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {42},
     number = {4},
     year = {2006},
     pages = {417-454},
     doi = {10.1016/j.anihpb.2005.06.002},
     zbl = {1104.35078},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2006__42_4_417_0}
}
Odasso, Cyril. Ergodicity for the stochastic complex Ginzburg-Landau equations. Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 4, pp. 417-454. doi : 10.1016/j.anihpb.2005.06.002. http://www.numdam.org/item/AIHPB_2006__42_4_417_0/

[1] M. Barton-Smith, Invariant measure for the stochastic Ginzburg Landau equation, NoDEA Nonlinear Differential Equations Appl. 11 (1) (2004) 29-52. | MR 2035365 | Zbl 1060.60062

[2] P. Bebouche, A. Jüngel, Inviscid limits of the Complex Ginzburg-Landau equation, Comm. Math. Phys. 214 (2000) 201-226. | MR 1794271 | Zbl 0978.35059

[3] J. Bricmont, A. Kupiainen, R. Lefevere, Exponential mixing for the 2D stochastic Navier-Stokes dynamics, Comm. Math. Phys. 230 (1) (2002) 87-132. | MR 1930573 | Zbl 1033.76011

[4] G. Da Prato, J. Zabczyk, Stochastic equations in infinite dimensions, in: Encyclopedia Math. Appl., Cambridge University Press, 1992. | MR 1207136 | Zbl 0761.60052

[5] A. De Bouard, A. Debussche, A stochastic non-linear Schrödinger equation with multiplicative noise, Comm. Math. Phys. 205 (1999) 161-181. | MR 1706888 | Zbl 0952.60061

[6] A. De Bouard, A. Debussche, The stochastic non-linear Schrödinger equation in H 1 , Stochastic Anal. Appl. 21 (1) (2003) 97-126. | MR 1954077 | Zbl 1027.60065

[7] W. E, J.C. Mattingly, Y.G. Sinai, Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation, Comm. Math. Phys. 224 (2001) 83-106. | MR 1868992 | Zbl 0994.60065

[8] V. Ginzburg, L. Landau, On the theorie of superconductivity, Zh. Eksp. Fiz. 20 (1950) 1064, English transl., in: Haar Ter (Ed.), Men of Physics: L.D. Landau, vol. I, Pergamon Press, New York, 1965, pp. 546-568.

[9] M. Hairer, Exponential mixing properties of stochastic PDEs through asymptotic coupling, Probab. Theory Related Fields 124 (3) (2002) 345-380. | MR 1939651 | Zbl 1032.60056

[10] G. Huber, P. Alstrom, Universal decay of vortex density in two dimensions, Physica A 195 (1993) 448-456. | Zbl 0803.76030

[11] S. Kuksin, On exponential convergence to a stationary measure for nonlinear PDEs, in: The M.I. Viishik Moscow PDE seminar, Amer. Math. Soc. Transl. Ser. (2), vol. 206, Amer. Math. Soc., 2002. | MR 1939491

[12] S. Kuksin, A. Shirikyan, Stochastic dissipative PDE's and Gibbs measures, Comm. Math. Phys. 213 (2000) 291-330. | MR 1785459 | Zbl 0974.60046

[13] S. Kuksin, A. Shirikyan, A coupling approach to randomly forced PDE's I, Comm. Math. Phys. 221 (2001) 351-366. | MR 1845328 | Zbl 0991.60056

[14] S. Kuksin, A. Piatnitski, A. Shirikyan, A coupling approach to randomly forced PDE's II, Comm. Math. Phys. 230 (1) (2002) 81-85. | MR 1927233 | Zbl 1010.60066

[15] S. Kuksin, A. Shirikyan, Coupling approach to white-forced nonlinear PDEs, J. Math. Pures Appl. 1 (2002) 567-602. | MR 1912412 | Zbl 1021.37044

[16] S. Kuksin, A. Shirikyan, Randomly forced CGL equation: Stationary measure and the inviscid limit, J. Phys. A 37 (12) (2004) 3805-3822. | MR 2039838 | Zbl 1047.35061

[17] J. Mattingly, Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics, Comm. Math. Phys. 230 (2002) 421-462. | MR 1937652 | Zbl 1054.76020

[18] J. Mattingly, On recent progress for the stochastic Navier-Stokes equations, in: Journées Équations aux Dérivées Partielles, Exp. No XI, vol. 52, Univ. Nantes, Nantes, 2003. | Numdam | MR 2050597 | Zbl 1044.58044

[19] A. Newel, J. Whitehead, Finite bandwidth, finite amplitude convection, J. Fluid Mech. 38 (1969) 279-303. | Zbl 0187.25102

[20] A. Newel, J. Whitehead, Review of the finite bandwidth concept, in: Leipholz H. (Ed.), Proceedings of the Internat. Union of Theor. and Appl. Math., Springer, Berlin, 1971, pp. 284-289. | Zbl 0247.76039

[21] C. Odasso, Propriétés ergodiques de l'équation de Ginzburg-Landau complexe bruitée, Mémoire de DEA, 2003.

[22] A. Shirikyan, Exponential mixing for 2D Navier-Stokes equation perturbed by an unbounded noise, J. Math. Fluid Mech. 6 (2) (2004) 169-193. | MR 2053582 | Zbl 1095.35032