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Rare events in the Boussinesq system with fluctuating dynamical boundary conditions. (English) Zbl 1183.35280
Summary: The Boussinesq system models various phenomena in geophysical and climate dynamics. It is a coupled system of the Navier-Stokes equations and the salinity transport equation. Due to uncertainty in salinity flux on fluid boundary, this system is subject to random fluctuations on the boundary. This stochastic Boussinesq system can be transformed into a random dynamical system. Rare events, or small probability events, are investigated in the context of large deviations. A large deviations principle is established via a weak convergence approach based on a recently developed variational representation of functionals of infinite dimensional Brownian motion.
MSC:
35R60PDEs with randomness, stochastic PDE
35Q35PDEs in connection with fluid mechanics
60H15Stochastic partial differential equations
76M35Stochastic analysis (fluid mechanics)
86A05Hydrology, hydrography, oceanography
86A10Meteorology and atmospheric physics
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