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Random attractors of Boussinesq equations with multiplicative noise. (English) Zbl 1209.37061

Consider Stratonovich-interpreted two-dimensional Boussinesq equation perturbed by multiplicative white noise

dv+[(v·)v-νΔv+p]dt=e 2 (T-T 1 )dt+bvdW(t)
div (v)=0

on the domain D=(0,1) 2 , where e i are the unit vectors of 2 . The authors prove the existence of a compact random attractor (i.e. a “pullback” attractor) for the random dynamical system (RDS) belonging to this stochastic differential equation (related to the Bénard flow problem).

37H10Generation, random and stochastic difference and differential equations
37L30Attractors and their dimensions, Lyapunov exponents
35Q30Stokes and Navier-Stokes equations
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