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Comptes Rendus Mathématique
Volume 343, n° 1
pages 47-50 (juillet 2006)
Doi : 10.1016/j.crma.2006.04.025
Received : 22 November 2005 ;  accepted : 27 April 2006
Markov selections and their regularity for the three-dimensional stochastic Navier-Stokes equations
Sélections Markoviennes et leur régularité pour les équations stochastiques de Navier-Stokes tridimensionnelles
 

Franco Flandoli a , Marco Romito b
a Dipartimento di Matematica Applicata, Università di Pisa, via Bonanno Pisano, 25/b, 56126 Pisa, Italy 
b Dipartimento di Matematica, Università di Firenze, viale Morgagni 67/a, 50134 Firenze, Italy 

Abstract

The martingale problem associated to the three-dimensional Navier-Stokes equations is shown to have a family of solutions satisfying the Markov property. The result is achieved by means of an abstract selection principle. The Markov property is crucial to extend the regularity of the transition semigroup from small times to arbitrary times, thus showing that every Markov selection has a property of continuous dependence on initial conditions. To cite this article: F. Flandoli, M. Romito, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.
Résumé

Il est établi que le problème de martingales associé aux équations de Navier-Stokes tridimensionnelles possède une famille de solutions qui satisfont la propriété de Markov. Ce résultat est obtenu par un principe abstrait de sélection. La propriété de Markov est fondamentale pour étendre la régularité du semi groupe de transition des petites échelles de temps à des échelles arbitraires, en établissant en particulier que chaque sélection de Markov dépend continûment des conditions initiales. Pour citer cet article : F. Flandoli, M. Romito, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.


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