On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations
Annales de l'I.H.P. Probabilités et statistiques, Volume 43 (2007) no. 4, p. 399-415
@article{AIHPB_2007__43_4_399_0,
     author = {Agrachev, Andrei A. and Kuksin, S. and Sarychev, A. and Shirikyan, A.},
     title = {On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {43},
     number = {4},
     year = {2007},
     pages = {399-415},
     doi = {10.1016/j.anihpb.2006.06.001},
     zbl = {pre05171264},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2007__43_4_399_0}
}
Agrachev, A.; Kuksin, S.; Sarychev, A.; Shirikyan, A. On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations. Annales de l'I.H.P. Probabilités et statistiques, Volume 43 (2007) no. 4, pp. 399-415. doi : 10.1016/j.anihpb.2006.06.001. http://www.numdam.org/item/AIHPB_2007__43_4_399_0/

[1] A.A. Agrachev, A.V. Sarychev, Navier-Stokes equations: controllability by means of low modes forcing, J. Math. Fluid Mech. 7 (1) (2005) 108-152. | Zbl 1075.93014

[2] A.A. Agrachev, A.V. Sarychev, Controllability of 2D Euler and Navier-Stokes equations by degenerate forcing, Comm. Math. Phys. 265 (2006) 673-697. | Zbl 1105.93008

[3] V.I. Bogachev, Gaussian Measures, Mathematical Surveys and Monographs, vol. 62, American Mathematical Society, Providence, RI, 1998. | MR 1642391 | Zbl 0938.28010 | Zbl 0913.60035

[4] V. Bally, E. Pardoux, Malliavin calculus for white noise driven parabolic SPDEs, Potential Anal. 9 (1) (1998) 27-64. | MR 1644120 | Zbl 0928.60040

[5] P. Constantin, C. Foias, Navier-Stokes Equations, University of Chicago Press, Chicago, IL, 1988. | Zbl 0687.35071

[6] R.C. Dalang, N.E. Frangos, The stochastic wave equation in two spatial dimensions, Ann. Probab. 26 (1) (1998) 187-212. | MR 1617046 | Zbl 0938.60046

[7] S. Dineen, Zero one laws for probability measures on locally convex spaces, Math. Ann. 243 (2) (1979) 95-102. | MR 543719 | Zbl 0393.60030

[8] J.-P. Eckmann, M. Hairer, Uniqueness of the invariant measure for a stochastic PDE driven by degenerate noise, Comm. Math. Phys. 219 (2001) 523-565. | MR 1838749 | Zbl 0983.60058

[9] W. Feller, An Introduction to Probability Theory and Its Applications, vol. II, John Wiley & Sons, New York, 1971. | MR 270403 | Zbl 0219.60003

[10] F. Flandoli, Dissipativity and invariant measures for stochastic Navier-Stokes equations, NoDEA 1 (1994) 403-426. | Zbl 0820.35108

[11] I.I. Gihman, A.V. Skorohod, The Theory of Stochastic Processes. I, Springer-Verlag, Berlin, 1980. | MR 636254 | Zbl 0531.60001

[12] R.Z. Has′Minskiĭ, Stochastic Stability of Differential Equations, Sijthoff & Noordhoff, Alphen aan den Rijn, 1980.

[13] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin, 1981. | MR 610244 | Zbl 0456.35001

[14] S.B. Kuksin, Diffeomorphisms of function spaces that correspond to quasilinear parabolic equations, Mat. Sb. (N.S.) 117 (159) (1982) 359-378, 431. | MR 648413 | Zbl 0501.35046

[15] J.A. León, D. Nualart, R. Pettersson, The stochastic Burgers equation: finite moments and smoothness of the density, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 3 (3) (2000) 363-385. | MR 1811248 | Zbl 0968.60057

[16] J. Mattingly, E. Pardoux, Malliavin calculus for the stochastic 2D Navier-Stokes equation, Comm. Pure Appl. Math. 59 (12) (2006) 1742-1790. | Zbl 1113.60058

[17] D. Nualart, The Malliavin Calculus and Related Topics, Springer-Verlag, New York, 1995. | MR 1344217 | Zbl 0837.60050

[18] D. Ocone, Stochastic calculus of variations for stochastic partial differential equations, J. Funct. Anal. 79 (2) (1988) 288-331. | MR 953905 | Zbl 0653.60046

[19] S. Sternberg, Lectures on Differential Geometry, Chelsea Publishing Co., New York, 1983. | MR 891190 | Zbl 0518.53001

[20] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam, 1979. | Zbl 0426.35003

[21] M.I. Vishik, A.V. Fursikov, Mathematical Problems in Statistical Hydromechanics, Kluwer, Dordrecht, 1988. | Zbl 0688.35077