Comptes Rendus
Probability Theory/Functional Analysis
A new approach to Kolmogorov equations in infinite dimensions and applications to the stochastic 2D Navier–Stokes equation
[Une nouvelle approche dans une infinité de dimensions et applications à l'équation Navier–Stokes stochastique en 2D]
Comptes Rendus. Mathématique, Volume 345 (2007) no. 5, pp. 289-292.

Dans cette Note nous présentons une nouvelle approche pour résoudre des équations de Kolmogorov à une infinité de variables dans des espaces à poids de fonctions faiblement continus. Le cas de coéfficients de diffusion non-constants et éventuellement dégénérés est inclus.

In this Note we present a new approach to solve Kolmogorov equations in infinitely many variables in weighted spaces of weakly continuous functions, including the case of non-constant possibly degenerate diffusion coefficients.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.07.009

Michael Röckner 1 ; Zeev Sobol 1

1 Department of Mathematics, Purdue University, West Lafayette, IN 47907-2, USA
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Michael Röckner; Zeev Sobol. A new approach to Kolmogorov equations in infinite dimensions and applications to the stochastic 2D Navier–Stokes equation. Comptes Rendus. Mathématique, Volume 345 (2007) no. 5, pp. 289-292. doi : 10.1016/j.crma.2007.07.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.07.009/

[1] F. Flandoli; M. Romito Markov selections and their regularity for the three-dimensional stochastic Navier–Stokes equations, C. R. Math. Acad. Sci. Paris, Ser. I, Volume 343 (2006), pp. 47-50

[2] M. Röckner; Z. Sobol Kolmogorov equations in infinite dimensions: well-posedness and regularity of solutions, with applications to stochastic generalized Burgers equations, Ann. Probab., Volume 34 (2006), pp. 663-727

[3] M. Röckner, Z. Sobol, Markov solutions for martingale problem: method of Lyapunov function, in preparation

[4] R. Stasi, m-dissipativity for 2D Navier–Stokes operators with periodic boundary conditions, in preparation

[5] D.W. Stroock; S.R.S. Varadhan Multidimensional Diffusion Processes, Grundlehren der Mathematischen Wissenschaften, Fundamental Principles of Mathematical Sciences, vol. 233, Springer-Verlag, Berlin–New York, 1979

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