Qualitative properties of stationary measures for three-dimensional Navier-Stokes equations

Journal of Functional Analysis

Volumn 249, Issue 2, 2007, Pages 284-306

  Shirikyan, Armen ^a  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

Author keywords

3D Navier Stokes system; Controllability; Irreducibility; Stationary solutions

Indexed keywords

EID: 34250657918     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2007.01.005     Document Type: Article

References (25)

1. Agrachev A., Kuksin S., Sarychev A., and Shirikyan A. On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations. Ann. Inst. H. Poincaré Probab. Statist. (2007) in press, available online 13 December 2006
2. Bensoussan A., and Temam R. Équations stochastiques du type Navier-Stokes. J. Funct. Anal. 13 (1973) 195-222
3. Bogachev V.I. Gaussian Measures (1998), Amer. Math. Soc., Providence, RI
4. Bogachev V.I. Measures on topological spaces. J. Math. Sci. (N.Y.) 91 4 (1998) 3033-3156
5. Brzeźniak Z. On analytic dependence of solutions of Navier-Stokes equations with respect to exterior force and initial velocity. Univ. Iagel. Acta Math. (28) (1991) 111-124
6. Capiński M., and Ga{ogonek}tarek D. Stochastic equations in Hilbert space with application to Navier-Stokes equations in any dimension. J. Funct. Anal. 126 1 (1994) 26-35
7. Da Prato G., and Debussche A. Ergodicity for the 3D stochastic Navier-Stokes equations. J. Math. Pures Appl. 82 (2003) 877-947
8. Flandoli F. Irreducibility of the 3-D stochastic Navier-Stokes equation. J. Funct. Anal. 149 1 (1997) 160-177
9. Flandoli F., and Ga{ogonek}tarek D. Martingale and stationary solutions for stochastic Navier-Stokes equations. Probab. Theory Related Fields 102 3 (1995) 367-391
10. F. Flandoli, M. Romito, Markov selections for the 3D stochastic Navier-Stokes equations, preprint, 2006, see http://web.math.unifi.it/users/romito/?s=2&ve=17
11. Fujita H., and Kato T. On the Navier-Stokes initial value problem. I. Arch. Ration. Mech. Anal. 16 (1964) 269-315
12. Kuksin S. Diffeomorphisms of function spaces that correspond to quasilinear parabolic equations. Mat. Sb. (N.S.) 117(159) 3 (1982) 359-378 431
13. Mattingly J., and Pardoux E. Malliavin calculus for the stochastic 2D Navier-Stokes equation. Comm. Pure Appl. Math. 59 (2006) 1742-1790
14. Odasso C. Exponential mixing for the 3D stochastic Navier-Stokes equations. Comm. Math. Phys. 270 1 (2007) 109-139
15. Reed M., and Simon B. Methods of Modern Mathematical Physics I. Functional Analysis (1980), Academic Press, New York
16. M. Romito, Existence of martingale and stationary suitable weak solutions for a stochastic Navier-Stokes equations, preprint, 2001, 23 p., see http://www.arxiv.org/abs/math.PR/0609318
17. Shirikyan A. Approximate controllability of three-dimensional Navier-Stokes equations. Comm. Math. Phys. 266 1 (2006) 123-151
18. Shirikyan A. Controllability of three-dimensional Navier-Stokes equations and applications. Sémin. Équ. Dériv. Partielles, 2005-2006 (2006), École Polytech., Palaiseau
19. Shirikyan A. Exact controllability in projections for three-dimensional Navier-Stokes equations. Ann. Inst. H. Poincaré Anal. Non Linéaire (2007) in press, available online 20 September 2006
20. Sohr H. The Navier-Stokes Equations (2001), Birkhäuser, Basel
21. Sternberg S. Lectures on Differential Geometry (1983), Chelsea, New York
22. Taylor M.E. Partial Differential Equations. I-III (1996), Springer-Verlag, New York
23. Temam R. Navier-Stokes Equations (1979), North-Holland, Amsterdam
24. Vishik M.I., and Fursikov A.V. Mathematical Problems in Statistical Hydromechanics (1988), Kluwer, Dordrecht
25. Vishik M.I., Komech A.I., and Fursikov A.V. Some mathematical problems of statistical hydromechanics. Russian Math. Surveys 34 (1979) 149-234