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Large deviations for the Boussinesq equations under random influences |
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| Authors: | Jinqiao Duan Annie Millet |
| Affiliation: | 1. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA;2. SAMOS-MATISSE, Centre d’Économie de la Sorbonne (UMR 8174), Université Paris 1, Centre Pierre Mendès France, 90 rue de Tolbiac, F-75634 Paris Cedex 13, France;3. Laboratoire de Probabilités et Modèles Aléatoires (UMR 7599), Universités Paris 6-Paris 7, Boîte Courrier 188, 4 place Jussieu, 75252 Paris Cedex 05, France |
| Abstract: | A Boussinesq model for the Bénard 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. |
| Keywords: | primary 60H15 60F10 secondary 35R60 76D05 76R05 |
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