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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)
dT+[(v·)T-κΔT)]dt=0
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).

MSC:
37H10Generation, random and stochastic difference and differential equations
37L30Attractors and their dimensions, Lyapunov exponents
34D45Attractors
35Q30Stokes and Navier-Stokes equations
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