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Random dynamics of the Boussinesq system with dynamical boundary conditions. (English) Zbl 1179.60043
A coupled system of the two-dimensional Navier-Stokes equations and the salinity transport equation with spatially correlated white noise on the boundary as well as in fluid is investigated. The noise affects the system through a dynamical boundary condition. This system may be considered as a model for gravity currents in oceanic fluids. The noise is due to uncertainty in salinity flux on fluid boundary. After transforming this system into a random dynamical system, we first obtain asymptotic estimates on system evolution, and then show that the long time dynamics is captured by a random attractor.
MSC:
60H15Stochastic partial differential equations
86A05Hydrology, hydrography, oceanography
34D35Stability of manifolds of solutions of ODE