Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics

Communications in Mathematical Physics

Volumn 230, Issue 3, 2002, Pages 421-462

  Mattingly, Jonathan C ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036026973     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-002-0688-1     Document Type: Article

References (22)

1. [BKL00] Bricmont, J., Kupiainen, A., Lefevere, R.: Ergodicity of the 2D Navier-Stokes equations with random forcing. Commun. Math. Phys. 224, 65-81 (2001)
2. [CF88] Constantin, P., Foiaş, C.: Navier-Stokes Equations. Chicago, IL: University of Chicago Press, 1988
3. [DPZ96] Da Prato, G., Zabczyk, J.: Ergodicity for Infinite Dimensional Systems. Cambridge: 1996
4. [Dud76] Dudley, R.M.: Probabilities and metrics. In: Convergence of Laws on Metric Spaces, with a View to Statistical Testing. Lecture Notes Series, No. 45, Mathematisk Institut, Aarhus: Aarhus Universitet, 1976
5. [Dur96] Durrett, R.: Probability: Theory and Examples. Second edition, Belmont, CA: Duxbury Press, 1996
6. [EH] Eckmann, J.P., Hairer, M.: Uniqueness of the invariant measure for a stochastic pde driven by degenerate noise. Preprint
7. [EM01] Weinan, E., Mattingly, J.C.: Ergodicity for the Navier-Stokes equation with degenerate random forcing: Finite-dimensional approximation. Commun. Pure Appl. Math. 54(11), 1386-1402 (2001)
8. [EMS01] E, W., Mattingly, J.C., Sinai, Y.G.: Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation. Commun. Math. Phys. 224, 83-106 (2001)
9. [Fer97] Ferrario, B.: Ergodic results for stochastic Navier-Stokes equation. Stochastics and Stochastics Reports 60(3-4), 271-288 (1997)
10. [Fla94] Flandoli, F.: Dissipativity and invariant measures for stochastic Navier-Stokes equations. NoDEA 1, 403-426 (1994)
11. [FM95] Flandoli, F., Maslowski, B.: Ergodicity of the 2-D Navier-Stokes equation under random perturbations. Commun. Math. Phys. 171, 119-141 (1995)
12. [Har56] Harris, T.E.: The existence of stationary measures for certain Markov processes. In: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954-1955, vol. II. Berkeley and Los Angeles: Univ. of California Press, 1956, pp. 113-124
13. [Has80] Hasminskiǐ, R.Z.: Stochastic Stability of Differential Equations. Alphen aanden Rijn: Sijthoff & Noordhoff, 1980. Translated from the Russian by D. Louvish
14. [KS] Kuksin, S., Shirikyan, A.: Private communication, December 2000
15. [KS00] Kuksin, S., Shirikyan, A.: Stochastic dissipative PDEs and Gibbs measures. Commun. Math. Phys. 213(2), 291-330 (2000)
16. [Mat98] Mattingly, J.C.: The Stochastically Forced Navier-Stokes Equations: Energy Estimates and Phase Space Contraction. PhD thesis, Princeton University, 1998
17. [Mat99] Mattingly, J.C.: Ergodicity of 2D Navier-Stokes equations with random forcing and large viscosity. Commun. Math. Phys. 206(2), 273-288 (1999)
18. [MSH01] Mattingly, J.C., Smart, A.M., Higham, D.J.: Ergodicity for SDEs and approximations: Locally lipschitz vector fields and degenerate noise. Submited, 2001
19. [MT93] Meyn, S.P., Tweedie, R.L.: Markov Chains and Stochastic Stability. Berlin-Heidelberg-New York: Springer-Verlag, 1993
20. [Pro90] Protter, P.: Stochastic Integration and Differential Equations: A new approach. Berlin-Heideiberg-New York: Springer-Verlag, 1990
21. [RY94] Revuz, D., Yor, M.: Continuous Martingales and Brownian Motion. Vol. 293 of Grundlehren der Mathematischen Wissenschaften. Berlin: Springer-Verlag, Second edition, 1994
22. [VF88] Vishik, M.J., Fursikov, A.V.: Mathematical Problems of Statistical Hydrodynamics. Dordrecht: Kluwer Academic Publishers, 1988. Updated version of Russian original of same name