Xu, Tiange; Zhang, Tusheng
On the small time asymptotics of the two-dimensional stochastic Navier-Stokes equations
Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 4 , p. 1002-1019
Zbl 1196.60119 | MR 2572161
doi : 10.1214/08-AIHP192
URL stable : http://www.numdam.org/item?id=AIHPB_2009__45_4_1002_0

Classification:  60H15,  60F10,  35Q30
Dans cet article, nous établissons un principe de grandes déviations en temps petit pour l'équation de Navier-Stokes bi-dimensionnelle stochastique conduite par un bruit multiplicatif. Celui-ci nécessite non seulement l'étude d'un bruit faible, mais aussi la compréhension des effets de dérives petites mais non bornées et non linéaires.
In this paper, we establish a small time large deviation principle (small time asymptotics) for the two-dimensional stochastic Navier-Stokes equations driven by multiplicative noise, which not only involves the study of the small noise, but also the investigation of the effect of the small, but highly nonlinear, unbounded drifts.

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