Ergodic properties of highly degenerate 2D stochastic Navier-Stokes equations

Comptes Rendus Mathematique

Volumn 339, Issue 12, 2004, Pages 879-882

  Hairer, Martin ^a   Mattingly, Jonathan C ^b  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b DUKE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 10644294512     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2004.09.035     Document Type: Article

References (19)

1. J. Bricmont A. Kupiainen R. Lefevere Ergodicity of the 2D Navier-Stokes equations with random forcing Commun. Math. Phys. 224 1 2001 65-81
2. J. Bricmont A. Kupiainen R. Lefevere Exponential mixing of the 2D stochastic Navier-Stokes dynamics Commun. Math. Phys. 230 1 2002 87-132
3. A. Cruzeiro Solutions et mesures invariantes pour des équations d'évolution stochastiques du type Navier-Stokes Exposition. Math. 7 1 1989 73-82
4. B. Ferrario Ergodic results for stochastic Navier-Stokes equation Stochastics Stochastics Rep. 60 3-4 1997 271-288
5. F. Flandoli Dissipativity and invariant measures for stochastic Navier-Stokes equations NoDEA 1 1994 403-426
6. F. Flandoli B. Maslowski Ergodicity of the 2-D Navier-Stokes equation under random perturbations Commun. Math. Phys. 171 1995 119-141
7. M. Hairer Exponential mixing properties of stochastic PDEs through asymptotic coupling Probab. Theory Related Fields 124 3 2002 345-380
8. M. Hairer J.C. Mattingly Ergodicity of the degenerate stochastic 2D Navier-Stokes equation June 2004 submitted for publication
9. M. Hairer J.C. Mattingly É. Pardoux Malliavin calculus for highly degenerate stochastic 2D Navier-Stokes equations submitted for publication
10. S. Kuksin A. Shirikyan Stochastic dissipative PDEs and Gibbs measures Commun. Math. Phys. 213 2 2000 291-330
11. S. Kuksin A. Shirikyan Coupling approach to white-forced nonlinear PDEs J. Math. Pures Appl. 81 6 2002 567-602
12. J.C. Mattingly The Stochastically forced Navier-Stokes equations: Energy estimates and phase space contraction PhD thesis, Princeton University, 1998
13. J.C. Mattingly Ergodicity of 2D Navier-Stokes equations with random forcing and large viscosity Commun. Math. Phys. 206 2 1999 273-288
14. J.C. Mattingly Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics Commun. Math. Phys. 230 3 2002 421-462
15. J.C. Mattingly On recent progress for the stochastic Navier Stokes equations in: Journées Équations aux dérivées partielles 2003 Forges-les-Eaux see http://www.math.sciences.univ-nantes.fr/edpa/2003/html/
16. J. C. Mattingly É. Pardoux Malliavin calculus and the randomly forced Navier Stokes equation 2004 submitted for publication
17. E. Weinan D. Liu Gibbsian dynamics and invariant measures for stochastic dissipative PDEs J. Statist. Phys. 108 5/6 2002 1125-1156
18. E. Weinan J.C. Mattingly Ya.G. Sinai Gibbsian dynamics and ergodicity for the stochastic forced Navier-Stokes equation Commun. Math. Phys. 224 1 2001 83-106
19. E. Weinan J.C. Mattingly Ergodicity for the Navier-Stokes equation with degenerate random forcing: Finite-dimensional approximation Commun. Pure Appl. Math. 54 11 2001 1386-1402