The existence of martingale solutions to the stochastic Boussinesq equations

A stochastic Boussinesq model for the B´enard problem is considered as a system of stochastic Navier-Stokes equations and transport equation in Rd−1 × [0, 1], d = 2, 3. The existence of a martingale solution is proved. The construction of the solution is based on the Faedo-Galerkin approximation and the compactness method.