Large deviations for the Boussinesq Equations under Random Influences

Jinqiao Duan (1) , Annie Millet (2, 3, 4, 5)

1 IIT - Laboratory for Stochastics and Dynamics
2 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
3 CES - Centre d'économie de la Sorbonne
4 SAMOS - Statistique Appliquée et MOdélisation Stochastique
5 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

A Boussinesq model for the Benard convection under random influences is considered as a system of stochastic partial differential equations. This is a coupled system of stochastic Navier-Stokes equations and the transport equation for temperature. Large deviations are proved, using a weak convergence approach based on a variational representation of functionals of infinite dimensional Brownian motion.

Mots clés: Boussinesq equations; Benard convection; large deviations; stochastic PDEs; stochastic Navier-Stokes equations; impact of noise on system evolution; multiplicative noise

Domaines: Probabilités [math.PR]

Jinqiao Duan, Annie Millet. Large deviations for the Boussinesq Equations under Random Influences. Stochastic Processes and their Applications, 2009, 119 (6), pp.2052-2081. ⟨10.1016/j.spa.2008.10.004⟩. ⟨hal-00250132v3⟩