The Kolmogorov equation associated to the stochastic Navier-Stokes equations in 2D

Infinite Dimensional Analysis, Quantum Probability and Related Topics

Volumn 7, Issue 2, 2004, Pages 163-182

  Barbu, Viorel ^a   Da Prato, Giuseppe ^b   Debussche, Arnaud ^c  

^a ALEXANDRU IOAN CUZA UNIVERSITY OF IASI   (Romania)

^b SCUOLA NORMALE SUPERIORE   (Italy)

^c UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Invariant measure; Kolmogorov equations; Stochastic Navier Stokes equation; Transition semi group

Indexed keywords

EID: 7444267892     PISSN: 02190257     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219025704001554     Document Type: Article

References (23)

1. S. Albeverio and M. Röckner, Stochastic differential equations in infinite dimensions: solutions via Dirichlet forms, Probab. Theory Rel. Fields 89 (1991) 347-386.
2. D. Bakry, L'hypercontractivité et son utilisation en théorie des semigroupes, Lectures on Probability Theory, Vol. 1581 (Springer-Verlag, 1994).
3. V. Barbu and G. Da Prato, The two phase stochastic Stefan problem, Probab. Theory Rel. Fields, to appear.
4. J. Bricmont, A. Kupiainen and R. Lefevere, Exponential mixing for the 2D stochastic Navier-Stokes dynamics, Commun. Math. Phys. 230 (2002) 87-132.
5. G. Da Prato and A. Debussche Maximal dissipativity of the Dirichlet operator corresponding to the Burgers equation, CMS Conf. Proc., Vol. 28 (Canadian Math. Society, 2000), pp. 145-170.
6. G. Da Prato, A. Debussche and B. Goldys, Invariant measures of nonsymmetric dissipative stochastic systems, Probab. Theory Rel. Fields 123 (2002) 355-380.
7. G. Da Prato and M. Röckner, Singular dissipative stochastic equations in Hilbert spaces, Probab. Theory Rel. Fields 124 (2002) 261-303.
8. G. Da Prato and L. Tubaro, Some results about dissipativity of Kolmogorov operators, Czech. Math. J. 51, (2001) 685-699.
9. G. Da Prato and J. Zabczyk, Ergodicity for Infinite Dimensional Systems, London Mathematial Society Lecture Notes, Vol. 229 (Cambridge Univ. Press, 1996).
10. J. D. Deuschel and D. Stroock, Large Deviations (Academic Press, 1984).
11. W. E. J. C. Mattingly and Y. G. Sinai, Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation, Commun. Math. Phys. 224 (2001) 83-106.
12. A. Eberle, Uniqueness and Non-Uniqueness of Singular Diffusion Operators, Lecture Notes in Mathematics, Vol. 1718 (Springer-Verlag, 1999).
13. F. Flandoli, Dissipativity and invariant measures for stochastic Navier-Stokes equations, NoDEA 1 (1994) 403-423.
14. F. Flandoli and B. Maslowski, Ergodicity of the 2-D Navier-Stokes equation under random perturbations, Commun. Math. Phys. 171 (1995) 119-141.
15. S. Kuksin and A. Shirikyan, Ergodicity for the randomly forced 2D Navier-Stokes equations, Math. Phys. Anal. Geom. 4 (2001) 27-46.
16. S. Kuksin and A. Shirikyan, A coupling approach to randomly forced randomly forced PDE's I, Commun. Math. Phys. 221 (2001) 351-366.
17. S. Kuksin, A. Piatnitski and A. Shirikyan, A coupling approach to randomly forced randomly forced PDE's II, Commun. Math. Phys. 230 (2002) 81-85.
18. G. Lumer and R. S. Phillips, Dissipative operators in a Banach space, Pac. J. Math. 11 (1961) 679-698.
19. Z. M. Ma and M. Röckner, Introduction to the Theory of (Non Symmetric) Dirichlet Forms (Springer-Verlag, 1992).
20. J. C. Mattingly, Ergodicty of 2D Navier-Stokes equations with random forcing and large viscosity, Commun. Math. Phys. 206 (1999) 273-288.
21. J. C. Mattingly, Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics, Commun. Math. Phys. 230 (2002) 421-462.
22. N. Masmoudi and L. S. Young, Ergodic theory of infinite dimensional systems with applications to dissipative parabolic PDE's, Commun. Math. Phys. 227 (2002) 461-481.
23. R. Temam, Navier-Stokes Equations (North-Holland, 1977).