Comptes Rendus
no. 5
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]

Présenté par : Paul Malliavin

Michael Röckner1 ; Zeev Sobol1
1 Department of Mathematics, Purdue University, West Lafayette, IN 47907-2, USA
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 
@article{CRMATH_2007__345_5_289_0,
     author = {Michael R\"ockner and Zeev Sobol},
     title = {A new approach to {Kolmogorov} equations in infinite dimensions and applications to the stochastic {2D} {Navier{\textendash}Stokes} equation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {289--292},
     publisher = {Elsevier},
     volume = {345},
     number = {5},
     year = {2007},
     doi = {10.1016/j.crma.2007.07.009},
     language = {en},
}
TY  - JOUR
AU  - Michael Röckner
AU  - Zeev Sobol
TI  - A new approach to Kolmogorov equations in infinite dimensions and applications to the stochastic 2D Navier–Stokes equation
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 289
EP  - 292
VL  - 345
IS  - 5
PB  - Elsevier
DO  - 10.1016/j.crma.2007.07.009
LA  - en
ID  - CRMATH_2007__345_5_289_0
ER  - 
%0 Journal Article
%A Michael Röckner
%A Zeev Sobol
%T A new approach to Kolmogorov equations in infinite dimensions and applications to the stochastic 2D Navier–Stokes equation
%J Comptes Rendus. Mathématique
%D 2007
%P 289-292
%V 345
%N 5
%I Elsevier
%R 10.1016/j.crma.2007.07.009
%G en
%F CRMATH_2007__345_5_289_0
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

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

A new approach to Kolmogorov equations in infinite dimensions and applications to stochastic generalized Burgers equations

Michael Röckner; Zeev Sobol

C. R. Math (2004)

Global gradient bounds for dissipative diffusion operators

Vladimir I. Bogachev; Giuseppe Da Prato; Michael Röckner; ...

C. R. Math (2004)