A large deviation principle for 2D stochastic Navier-Stokes equation

Stochastic Processes and their Applications

Volumn 117, Issue 7, 2007, Pages 904-927

  Gourcy, Mathieu ^a  

^a UNIVERSITÉ BLAISE PASCAL   (France)

Author keywords

Large deviations; Occupation measure; Stochastic Navier Stokes equation

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; RANDOM PROCESSES; STATISTICAL METHODS;

EXPONENTIAL CONVERGENCE; STOCHASTIC NAVIER STOKES EQUATION;

NAVIER STOKES EQUATIONS;

EID: 34248595141     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2006.11.001     Document Type: Article

References (29)

1. Amirdjanova A., and Xiong J. Large deviation principle for a stochastic Navier-Stokes equation in its vorticity form for a two-dimensional incompressible flow. Discrete Contin. Dyn. Syst. Ser. B 6 (2006) 651-666
2. Bensoussan A., and Temam R. Equations stochastiques du type Navier-Stokes. J. Funct. Anal. 13 (1973) 195-222
3. Capinski M., and Gatarek D. Stochastic equations in Hilbert space with application to Navier-Stokes equations in any dimension. J. Funct. Anal. 126 (1994) 26-35
4. Chang M.H. Large deviation for Navier-Stokes equations with small stochastic perturbation. Appl. Math. Comput. 76 (1996) 65-93
5. Collina R., Livi R., and Mazzino A. Large deviation approach to the randomly forced Navier-Stokes equation. J. Stat. Phys. 118 (2005) 451-479
6. Da Prato G., and Debussche A. Ergodicity for the 3D stochastic Navier-Stokes equations. J. Math. Pures Appl. 82 (2003) 877-947
7. Da Prato G., and Zabczyk J. Ergodicity for Infinite Dimensional Systems (1996), Cambridge University Press
8. Dembo A., and Zeitouni O. Large Deviations Techniques and Applications. 2nd ed. (1998), Springer-Verlag
9. Deuschel J.D., and Stroock D.W. Large Deviations. Pure Appl. Math. vol. 137 (1989), Academic Press, San Diego
10. Donsker M.D., and Varadhan S.R.S. Asymptotic evalutation of certain Markov process expectations for large time, I-IV. Comm. Pure Appl. Math. 28 (1975) 1-47 279-301; 29 (1976) 389-461; 36 (1983) 183-212
11. Weinan E., Mattingly J.C., and Sinai Y.G. Gibbsian dynamics and ergodicity for the stochastic forced Navier-Stokes equation. Comm. Math. Phys. 224 (2002) 83-106
12. Ferrario B. Ergodic results for stochastic Navier-Stokes equations. Stoch. Stoch. Rep. 60 (1997) 271-288
13. Ferrario B. Stochastic Navier-Stokes equations: Analysis of the noise to have a unique invariant measure. Ann. Mat. Pura Appl. (IV) CLXXVII (1999) 331-347
14. Flandoli F. Dissipativity and invariant measures for stochastic Navier-Stokes equations. NoDEA 1 (1994) 403-428
15. Flandoli F., and Gatarek D. Martingale and stationary solutions for stochastic Navier-Stokes equations. Probab. Theory Related Fields 102 (1995) 367-391
16. Flandoli F., and Maslowski B. Ergodicity of the 2D Navier-Stokes equation under random perturbation. Comm. Math. Phys. 171 (1995) 119-141
17. Foias C., Manley O., Rosa R., and Temam R. Navier-Stokes Equations and Turbulence (2001), Cambridge University Press
18. Goldys B., and Maslowski B. Exponential ergodicity for stochastic burgers and 2D Navier-Stokes equation. J. Funct. Anal. 1 (2005) 230-255
19. M. Gourcy, Large deviation principle of occupation measure for stochastic burgers equation, Ann. Inst. H. Poincaré (2006) (in press)
20. M. Gourcy, Inégalités Log-Sobolev pour la loi d'une diffusion et Grandes déviations pour des EDP stochastiques, Ph.D. Thesis, Université Blaise Pascal, 2006
21. Hairer M., Mattingly J.C., and Pardoux E. Malliavin calculus for highly degenerate 2D stochastic Navier-Stokes equations. C. R. Math. Acad. Sci. Paris 339 11 (2004) 793-796
22. M. Hairer, J.C. Mattingly, Spectral gaps in wasserstein distances and the 2D Navier-Stokes equations, 2006 Preprint
23. Kuksin S., and Shirikyan A. Stochastic dissipative PDE's and gibbs measures. Comm. Math. Phys. 213 (2000) 291-330
24. Mattingly J.C. Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics. Comm. Math. Phys. 230 3 (2002) 421-462
25. C. Odasso, Méthodes de couplage pour des équations stochastiques du type Navier-Stokes et Schrödinger, Ph.D. Thesis, Université de Rennes 1, 2005
26. Sritharan S.S., and Sundar P. Large deviations for the two-dimensional Navier-Stokes equation with multiplicative noise. Stochastic Process. Appl. 116 (2006) 1636-1659
27. Temam R. Navier-Stokes Equations (1977), North-Holland
28. Wu L. Uniformly integrable operators and large deviations for Markov processes. J. Funct. Anal. 172 (2000) 301-376
29. Wu L. Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems. Stochastic Process. Appl. 91 (2001) 205-238