Exponential mixing for a stochastic partial differential equation driven by degenerate noise

Nonlinearity

Volumn 15, Issue 2, 2002, Pages 271-279

  Hairer, M ^a  

^a UNIVERSITY OF GENEVA   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013532163     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/15/2/304     Document Type: Article

References (21)

1. [BKL00a] Bricmont J, Kupiainen A and Lefevere R 2000 Exponential mixing of the 2D stochastic Navier-Stokes dynamics Preprint
2. [BKL00b] Bricmont J, Kupiainen A and Lefevere R 2000 Probabilistic estimates for the two dimensional stochastic Navier-Stokes equations J. Stat. Phys. nos (3-4) 743-56
3. [Cer99] Cerrai S 1999 Ergodicity for stochastic reaction-diffusion systems with polynomial coefficients Stochastics Stochastics Rep. 67 17-51
4. [Doe38] Doeblin W 1938 Exposé sur la théorie des chaînes simples constantes de Markoff àun nombre fini d'états Rev. Math. Union Interbalkanique 2 77-105
5. [Doo53] Doob J L 1953 Stochastic Processes (New York: Wiley)
6. [DPZ96] Da Prato G and Zabczyk J 1996 Ergodicity for Infinite Dimensional Systems (London Mathematical Society Lecture Note Series vol 229) (Cambridge: Cambridge University Press)
7. [EH01] Eckmann J-P and Hairer M 2001 Uniqueness of the invariant measure for a stochastic PDE driven by degenerate noise Commun. Math. Phys. 219 523-65
8. [EMS01] E W, Mattingly J C and Sinai Y G 2001 Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation Commun. Math. Phys. 224 83-106
9. [Fer95] Ferrario B 1995 Ergodic results for stochastic Navier-Stokes equation Stock. Stoch. Rep. 60 271-88
10. [FM95] Flandoli F and Maslowski B 1995 Ergodicity of the 2-D Navier-Stokes equation under random perturbations Commun. Math. Phys. 172 119-41
11. [GM01] Goldys B and Maslowski B 2001 Uniform exponential ergodicity of stochastic dissipative systems Czech. Math. J. submitted
12. [Har56] Harris T E 1956 The existence of stationary measures for certain Markov processes Proc. 3rd Berkeley Symp. on Mathematical Statistics and Probability (1954-1955) vol II (Berkeley, CA: University of California Press) pp 113-24
13. [Hör67] Hörmander L 1967 Hypoelliptic second order differential equations Acta Math. 119 147-71
14. [Hör85] Hörmander L 1985 The Analysis of Linear Partial Differential Operators 1-IV, (New York: Springer)
15. [KS00] Kuksin S B and Shirikyan A 2000 Stochastic dissipative PDE's and Gibbs measures Commun. Math. Phys. 213 291-30
16. [KS01] Kuksin S B and Shirikyan A 2001 A coupling approach to randomly forced nonlinear PDE's. I Commun. Math. Phys. 221 351-66
17. [Mat01] Mattingly J C 2001 Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics Preprint
18. [MS99] Maslowski B and Seidler J 1999 Invariant measures for nonlinear SPDE's: uniqueness and stability Archiv. Math. 34 153-72
19. [MT94] Meyn S P and Tweedie R L 1994 Markov Chains and Stochastic Stability (New York: Springer)
20. [Ore71] Orey S 1971 Lecture Notes on Limit Theorems for Markov Chain Transition Probabilities (Van Nostrand Reinhold Mathematical Studies No 34) (London: Van Nostrand Reinhold)
21. [RBT01] Rey-Bellet L and Thomas L 2001 Exponential convergence to non-equilibrium stationary states in classical statistical mechanics Preprint