[Une nouvelle approche dans une infinité de dimensions et applications à l'équation Navier–Stokes stochastique en 2D]
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.
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@article{CRMATH_2007__345_5_289_0,
author = {R\"ockner, Michael and Sobol, Zeev},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2007.07.009/}
}
TY - JOUR AU - Röckner, Michael AU - Sobol, Zeev 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2007.07.009/ DO - 10.1016/j.crma.2007.07.009 LA - en ID - CRMATH_2007__345_5_289_0 ER -
%0 Journal Article %A Röckner, Michael %A Sobol, Zeev %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 %U http://www.numdam.org/articles/10.1016/j.crma.2007.07.009/ %R 10.1016/j.crma.2007.07.009 %G en %F CRMATH_2007__345_5_289_0
Röckner, Michael; Sobol, Zeev. A new approach to Kolmogorov equations in infinite dimensions and applications to the stochastic 2D Navier–Stokes equation. Comptes Rendus. Mathématique, Tome 345 (2007) no. 5, pp. 289-292. doi : 10.1016/j.crma.2007.07.009. http://www.numdam.org/articles/10.1016/j.crma.2007.07.009/
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[3] M. Röckner, Z. Sobol, Markov solutions for martingale problem: method of Lyapunov function, in preparation
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