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Large deviations for the Boussinesq equations under random influences. (English) Zbl 1163.60315
Summary: 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.
##### MSC:
 60H15 Stochastic partial differential equations 60F10 Large deviations 35R60 PDEs with randomness, stochastic PDE 76D05 Navier-Stokes equations (fluid dynamics) 76R05 Forced convection (fluid mechanics)
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