Irreducibility of the 3-D stochastic Navier-Stokes equation

Journal of Functional Analysis

Volumn 149, Issue 1, 1997, Pages 160-177

  Flandoli, Franco ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031232487     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1996.3089     Document Type: Article

References (38)

1. Adams R. A. Sobolev Spaces. 1975;Academic Press, New York.
2. Albeverio S., Cruzeiro A. B. Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two dimensional fluids. Comm. Math. Phys. 129:1990;431-444.
3. Bensoussan A., Temam R. Equations stochastiques du type Navier-Stokes. J. Funct. Anal. 13:1973;195-222.
4. Brzezniak Z., Capinski M., Flandoli F. Stochastic Navier-Stokes equations with multiplicative noise. Stochastic Anal. Appl. 10:1992;523-532.
5. Capinski M., Gatarek D. Stochastic equations in Hilbert space with application to Navier-Stokes equations in any dimension. J. Funct. Anal. 126:1994;26-35.
6. Chow P. L. Stochastic partial differential equations in turbolence related problems. Prob. Anal. and Related Topics. 1978;Academic Press. p. 1-43.
7. Crauel H., Flandoli F. Dissipativity of three-dimensional stochastic Navier-Stokes equation. Prog. Probab. 36:1995;67-76.
8. Cruzeiro A. B. Solutions et measures invariants pour des equations stochastiques du type Navier-Stokes. Exposition. Math. 7:1989;73-82.
9. Da Prato G., Zabczyk J. Stochastic Equations in Infinite Dimensions. 1992;Cambridge Univ. Press, Cambridge.
10. Doob J. L. Asymptotic properties of Markov transition probability. Trans. Am. Math. Soc. 64:1948;393-421.
11. Ferrario B. Ergodic results for stochastic Navier-Stokes equations. Stochastics Stochastics Rep. 60:1997;271-288.
12. Flandoli F. Dissipativity and invariant measures for stochastic Navier-Stokes equations. Nonlinear Differential Equations Appl. 1:1994;403-423.
13. Flandoli F. Stochastic differential equations in fluid dynamics. Rend. Sem. Mat. Fis. Milano. 1996.
14. Flandoli F., Gatarek D. Martingale and stationary solutions for stochastic Navier-Stokes equations. Probab. Theory Related Fields. 102:1995;367-391.
15. Flandoli F., Maslowski B. Ergodicity of the 2-D Navier-Stokes equation under random perturbations. Comm. Math. Phys. 171:1995;119-141.
16. Flandoli F., Schmalfuss B. Attractors for the stochastic 3D Navier-Stokes equation with multiplicative white noise. Stochastics Stochastic Reports. 59:1996;21-45.
17. F. Flandoli, B. Schmalfuss, Weak solutions and attractors for the 3D Navier-Stokes equation with non-regular force, J. Dynamics & Differential Equations.
18. Yashima H. Fujita. Equations de Navier-Stokes stochastiques non Homogenes et applications. 1992;Scuola Normale Superiore, Pisa.
19. Fursikov A. V. Control problems and theorems concerning the unique solvability of a mixed boundary value problem for the three-dimensional Navier-Stokes and Euler equations. Math. USSR Sbornik. 43:1982;251-273.
20. Fursikov A V. Statistical extremal problems and unique solvability of the three dimensional Navier-Stokes system under almost all initial conditions. Prikl. Matem. Mekhan. USSR. 46:1983;637-644.
21. Holmes P. Can dynamical systems approach turbulence? Lumley. Whither Turbulence? Turbulence at the Crossroad. 1991;Springer-Verlag, Berlin.
22. Khas'minskii R. Z. Ergodic properties of recurrent diffusion processes and stabilization of the solutions to the Cauchy problem for parabolic equations. Theory Probab. Appl. 5:1960;179-196.
23. Kotelenez P. A stochastic Navier-Stokes equation for the vorticity of a two-dimensional fluid. Ann. Probab. 5:1995;1126-1160.
24. Lions P. L. Incompressible Models. Mathematical Topics in Fluid Mechanics. 1:1996.
25. Lions J. L., Magenes E. Non-Homogeneous Boundary Value Problems and Applications. 1972;Springer-Verlag, Berlin.
26. Maslowski B. On probability distributions of solutions of semilinear stochastic evolution equations. Stochastics. 45:1993;17-44.
27. Monin A. S., Yaglom A. M. Statistical Fluid Mechanics: Mechanics of Turbulence. 1975;M.I.T. Press, Cambridge.
28. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. 1983;Springer-Verlag, Berlin.
29. Peszat S., Zabczyk J. Strong Feller property and irreducibility for diffusions on Hilbert spaces. Inst. Math. Polish. Acad. Sci. 510:1993.
30. Strauss W. A. On continuity of functions with values in various Banach spaces. Pacific J. Math. 19:1966;543-551.
31. Seidler J. Ergodic behaviour of stochastic parabolic equations. Czechoslovak Math. J. 47:1997.
32. Stettner L. Remarks on ergodic conditions for Markov processes on Polish spaces. Bull. Polish Acad. Sci. Math. 42:1994;103-114.
33. Stroock D. W., Varadhan S. R. S. Multidimensional Diffusion Processes. 1979;Springer- Verlag.
34. Temam R. The Navier-Stokes Equations. 1977;North Holland, Amsterdam.
35. Temam R. Navier-Stokes Equations and Nonlinear Functionals Analysis. 1983;SIAM, Philadelphia.
36. Temam R. Infinite Dimensional Dynamical Systems in Mechanics and Physics. 1988;Sprinter-Verlag.
37. M. Viot, 1976, Solutions Faibles d'Equations aux Derivees Partielles Stochastiques non Lineaires.
38. Vishik M. I., Fursikov A. V. Mathematical Problems of Statistical Hydromechanics. 1980;Kluwer, Dordrecht.