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.
Mots clés : stochastic Navier-Stokes equation, small time asymptotics, large deviation principle
@article{AIHPB_2009__45_4_1002_0, author = {Xu, Tiange and Zhang, Tusheng}, title = {On the small time asymptotics of the two-dimensional stochastic {Navier-Stokes} equations}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {1002--1019}, publisher = {Gauthier-Villars}, volume = {45}, number = {4}, year = {2009}, doi = {10.1214/08-AIHP192}, mrnumber = {2572161}, zbl = {1196.60119}, language = {en}, url = {http://www.numdam.org/articles/10.1214/08-AIHP192/} }
TY - JOUR AU - Xu, Tiange AU - Zhang, Tusheng TI - On the small time asymptotics of the two-dimensional stochastic Navier-Stokes equations JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2009 SP - 1002 EP - 1019 VL - 45 IS - 4 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/08-AIHP192/ DO - 10.1214/08-AIHP192 LA - en ID - AIHPB_2009__45_4_1002_0 ER -
%0 Journal Article %A Xu, Tiange %A Zhang, Tusheng %T On the small time asymptotics of the two-dimensional stochastic Navier-Stokes equations %J Annales de l'I.H.P. Probabilités et statistiques %D 2009 %P 1002-1019 %V 45 %N 4 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/08-AIHP192/ %R 10.1214/08-AIHP192 %G en %F AIHPB_2009__45_4_1002_0
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, pp. 1002-1019. doi : 10.1214/08-AIHP192. http://www.numdam.org/articles/10.1214/08-AIHP192/
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