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.
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.
Accepted:
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Michael Röckner 1; Zeev Sobol 1
@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/
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[2] 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
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