Essential m-dissipativity of Kolmogorov operators corresponding to periodic 2⁢D-Navier Stokes equations
Barbu, Viorel ; Da Prato, Giuseppe ; Debussche, Arnaud
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 15 (2004), p. 29-38 / Harvested from Biblioteca Digitale Italiana di Matematica
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We prove the essential m-dissipativity of the Kolmogorov operator associated with the stochastic Navier-Stokes flow with periodic boundary conditions in a space L2⁢H,ν where ν is an invariant measure

Si dimostra l’essenziale m-dissipatività dell’operatore di Kolmogorov associato al flusso dell’equazione di Navier-Stokes stocastica con condizioni periodiche in uno spazio L2⁢H,ν dove ν è una misura invariante.

Publié le : 2004-03-01
@article{RLIN_2004_9_15_1_29_0,
     author = {Viorel Barbu and Giuseppe Da Prato and Arnaud Debussche},
     title = {Essential m-dissipativity of Kolmogorov operators corresponding to periodic $2D$-Navier Stokes equations},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {15},
     year = {2004},
     pages = {29-38},
     zbl = {1096.35126},
     mrnumber = {2102747},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2004_9_15_1_29_0}
}

Barbu, Viorel; Da Prato, Giuseppe; Debussche, Arnaud. Essential m-dissipativity of Kolmogorov operators corresponding to periodic $2D$-Navier Stokes equations. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 15 (2004) pp. 29-38. http://gdmltest.u-ga.fr/item/RLIN_2004_9_15_1_29_0/

[1] Barbu, V. - Da Prato, G., The transition semigroup of stochastic Navier-Stokes equations in 2⁢D. Infinite Dimensional Analysis, Quantum Probability and related topics, to appear.

[2] Bricmont, J. - Kupiainen, A. - Lefevere, R., Exponential mixing of the 2⁢D stochastic Navier-Stokes dynamics. Commun. Math. Phys., 230, n. 1, 2002, 87-132. | MR 1930573 | Zbl 1033.76011

[3] Cerrai, S., A Hille-Yosida theorem for weakly continuous semigroups. Semigroup Forum, 49, 1994, 349-367. | MR 1293091 | Zbl 0817.47048

[4] Da Prato, G. - Tubaro, L., Some results about dissipativity of Kolmogorov operators. Czechoslovak Mathematical Journal, 51, 126, 2001, 685-699. | MR 1864036 | Zbl 0996.47028

[5] Da Prato, G. - Zabczyk, J., Second Order Partial Differential Equations in Hilbert spaces. London Mathematical Society Lecture Notes n. 293, Cambridge University Press, 2002. | MR 1985790 | Zbl 1012.35001

[6] Flandoli, F., Dissipativity and invariant measures for stochastic Navier-Stokes equations. NoDEA, 1, 1994, 403-423. | MR 1300150 | Zbl 0820.35108

[7] Flandoli, F. - Maslowski, B., Ergodicity of the 2⁢D Navier-Stokes equation under random perturbations. Commun. Math. Phys., 171, 1995, 119-141. | MR 1346374 | Zbl 0845.35080

[8] Kuksin, S. - Shirikyan, A., A coupling approach to randomly forced nonlinear PDE’s. I. Commun. Math. Phys., 221, n. 2, 2001, 351-366. | MR 1845328 | Zbl 0991.60056

[9] Kuksin, S. - Piatniski, A. - Shirikyan, A., A coupling approach to randomly forced nonlinear PDE’s. II. Commun. Math. Phys., 230, n. 1, 2002, 81-85. | MR 1927233 | Zbl 1010.60066

[10] Temam, R., Navier-Stokes equations. Theory and numerical analysis. North-Holland, 1977. | Zbl 0568.35002

[11] Weinan, E. - Mattingly, J.C. - Sinai, Ya., Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation. Commun. Math. Phys., 224, n. 1, 2001, 83-106. | MR 1868992 | Zbl 0994.60065