Random attractors of Boussinesq equations with multiplicative noise (Q1034272)

Consider Stratonovich-interpreted two-dimensional Boussinesq equation perturbed by multiplicative white noise \[ dv + [(v \cdot \nabla) v - \nu \Delta v + \nabla p] dt = e_2(T-T_1) dt + bv \circ dW(t) \] \[ dT+[(v \cdot \nabla)T-\kappa \Delta T)] dt = 0 \] \[ \mathrm{div}(v) = 0 \] on the domain \(D = (0,1)^2\), where \(e_i\) are the unit vectors of \(\mathbb{R}^2\). 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).