Essential m-dissipativity of Kolmogorov operators corresponding to periodic 2 ⁢ D -Navier Stokes equations

Viorel Barbu; Giuseppe Da Prato; Arnaud Debussche

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2004)

  • Volume: 15, Issue: 1, page 29-38
  • ISSN: 1120-6330

Abstract

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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 L 2 ⁢ H , ν where ν is an invariant measure

How to cite

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Barbu, Viorel, Da Prato, Giuseppe, and 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 15.1 (2004): 29-38. <http://eudml.org/doc/252438>.

@article{Barbu2004,
abstract = {We prove the essential m-dissipativity of the Kolmogorov operator associated with the stochastic Navier-Stokes flow with periodic boundary conditions in a space $L^\{2\}(H,\nu)$ where $\nu$ is an invariant measure},
author = {Barbu, Viorel, Da Prato, Giuseppe, Debussche, Arnaud},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Stochastic Navier-Stokes equations; Kolmogorov operators; Invariant measures; invariant measures},
language = {eng},
month = {3},
number = {1},
pages = {29-38},
publisher = {Accademia Nazionale dei Lincei},
title = {Essential m-dissipativity of Kolmogorov operators corresponding to periodic $2D$-Navier Stokes equations},
url = {http://eudml.org/doc/252438},
volume = {15},
year = {2004},
}

TY - JOUR
AU - Barbu, Viorel
AU - Da Prato, Giuseppe
AU - Debussche, Arnaud
TI - Essential m-dissipativity of Kolmogorov operators corresponding to periodic $2D$-Navier Stokes equations
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/3//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 1
SP - 29
EP - 38
AB - We prove the essential m-dissipativity of the Kolmogorov operator associated with the stochastic Navier-Stokes flow with periodic boundary conditions in a space $L^{2}(H,\nu)$ where $\nu$ is an invariant measure
LA - eng
KW - Stochastic Navier-Stokes equations; Kolmogorov operators; Invariant measures; invariant measures
UR - http://eudml.org/doc/252438
ER -

References

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  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. Zbl1033.76011MR1930573DOI10.1007/s00220-002-0708-1
  3. CERRAI, S., A Hille-Yosida theorem for weakly continuous semigroups. Semigroup Forum, 49, 1994, 349-367. Zbl0817.47048MR1293091DOI10.1007/BF02573496
  4. DA PRATO, G. - TUBARO, L., Some results about dissipativity of Kolmogorov operators. Czechoslovak Mathematical Journal, 51, 126, 2001, 685-699. Zbl0996.47028MR1864036DOI10.1023/A:1013704610695
  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. Zbl1012.35001MR1985790DOI10.1017/CBO9780511543210
  6. FLANDOLI, F., Dissipativity and invariant measures for stochastic Navier-Stokes equations. NoDEA, 1, 1994, 403-423. Zbl0820.35108MR1300150DOI10.1007/BF01194988
  7. FLANDOLI, F. - MASLOWSKI, B., Ergodicity of the 2 ⁢ D Navier-Stokes equation under random perturbations. Commun. Math. Phys., 171, 1995, 119-141. Zbl0845.35080MR1346374
  8. KUKSIN, S. - SHIRIKYAN, A., A coupling approach to randomly forced nonlinear PDE’s. I. Commun. Math. Phys., 221, n. 2, 2001, 351-366. Zbl0991.60056MR1845328DOI10.1007/s002200100479
  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. Zbl1010.60066MR1927233DOI10.1007/s00220-002-0707-2
  10. TEMAM, R., Navier-Stokes equations. Theory and numerical analysis. North-Holland, 1977. Zbl0568.35002
  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. Zbl0994.60065MR1868992DOI10.1007/s002201224083

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