Exponential mixing for 2D Navier-Stokes equations perturbed by an unbounded noise

Journal of Mathematical Fluid Mechanics

Volumn 6, Issue 2, 2004, Pages 169-193

  Shirikyan, Armen ^a  

^a UNIVERSITÉ PARIS SUD   (France)

Author keywords

Coupling; Exponential mixing; Navier Stokes equations

Indexed keywords

BOUNDARY CONDITIONS; MARKOV PROCESSES; PARTIAL DIFFERENTIAL EQUATIONS; PROBABILITY; RANDOM PROCESSES;

COUPLING APPROACH; DIRICHLET BOUNDARY CONDITION; EXPONENTIAL MIXING; HILBERT SPACE;

NAVIER STOKES EQUATIONS;

EID: 4544351685     PISSN: 14226928     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00021-003-0088-0     Document Type: Article

References (26)

1. A. A. BOROVKOV, Ergodicity and Stability of Stochastic Processes, John Wiley & Sons, Chichester, 1998.
2. J. BRICMONT, A. KUPIAINEN AND R. LEFBVERE, Ergodicity of the 2D Navier-Stokes equations with random forcing, Comm. Math. Phys. 224 (2001), 65-81.
3. J. BRICMONT, A. KUPIAINEN AND R. LEFEVERE, Exponential mixing for the 2D stochastic Navier-Stokes dynamics, Comm. Math. Phys. 230 (2002), 87-132.
4. P. CONSTANTIN AND C. FOIAS, Navier-Stokes Equations, University of Chicago Press, Chicago, IL, 1988.
5. R. M. DUDLEY, Real Analysis and Probability, Wadsworth & Brooks/Cole, Pacific Grove, CA, 1989.
6. W. E. J. C. MATTINGLY AND YA. G. SINAI, Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation, Comm. Math. Phys. 224 (2001), 83-106.
7. J.-P. ECKMANN AND M. HAIRER, Uniqueness of the invariant measure for a stochastic PDE driven by degenerate noise, Comm. Math. Phys. 219 (2001), 523-565.
8. F. PLANDOLI AND B. MASLOWSKI, Ergodicity of the 2-D Navier-Stokes equation under random perturbations, Comm. Math. Phys. 172 (1995), 119-141.
9. C. FOIAş AND G. PRODI, Sur le comportement global des solutions non-stationnaires des équations de Navier-Stokes en dimension 2, Rend. Sem. Mat. Univ. Padova 39 (1967), 1-34.
10. R. Z. HAS'MINSKIǏ, Stochastic Stability of Differential Equations, Sijthoff & Noordhoff, Alphen aan den Rijn, 1980.
11. M. HAIRER, Exponential mixing properties of stochastic PDE's through asymptotic coupling, preprint (2001).
12. S. KUKSIN, On exponential convergence to a stationary measure for nonlinear PDE's, perturbed by random kick-forces, and the turbulence-limit, The M. I. Vishik Moscow PDE seminar, AMS Translations, 2002.
13. S. KUKSIN, Ergodic theorems for 2D statistical hydrodynamics, Rev. Math. Physics 14 (2002), 585-600.
14. S. KUKSIN AND A. SHIRIKYAN, Stochastic dissipative PDE's and Gibbs measures, Comm. Math. Phys. 213 (2000), 291-330.
15. S. KUKSIN AND A. SHIRIKYAN, Ergodicity for the randomly forced 2D Navier-Stokes equations, Math. Phys. Anal. Geom. 4 (2001), 147-195.
16. S. KUKSIN AND A. SHIRIKYAN, A coupling approach to randomly forced nonlinear PDE's. I, Comm. Math. Phys. 221 (2001), 351-366.
17. S. KUKSIN, A. PIATNITSKI AND A. SHIRIKYAN, A coupling approach to randomly forced nonlinear PDE's. II, Comm. Math. Phys. 230 (2002), 81-85.
18. S. KUKSIN AND A. SHIRIKYAN, Coupling approach to white-forced nonlinear PDE's, J. Math. Pures Appl. 81 (2002), 567-602.
19. N. MASMOUDI AND L.-S. YOUNG, Ergodic theory of infinite dimensional systems with applications to dissipative parabolic PDEs, Comm. Math. Phys. 227 (2002), 461-481.
20. J. C. MATTINGLY, Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics, preprint (2001).
21. B. ØKSENDAL, Stochastic Differential Equations, Springer-Verlag, Berlin, 1998.
22. D. REVUZ, Markov Chains, North-Holland, Amsterdam, New York, Oxford, 1984.
23. A. SHIRIKYAN, Analyticity of solutions for randomly forced two-dimensional Navier-Stokes equations, Russian Math. Surveys, to appear.
24. D. W. STROOCK, Probability Theory. An Analytic View, Cambridge University Press, Cambridge, 1993.
25. R. TEMAM, Navier-Stokes Equations. Theory and Numerical Analysis, North-Holland, Amsterdam, New York, Oxford, 1977.
26. A. Yu. VERETENNIKOV, Parametric and Non-Parametric Estimation of Markov Chains, Moscow State University Press, Moscow, 2000 (in Russian).