Asymptotic behaviour of solutions to the exterior problem for the Oberbeck-Boussinesq equations

The authors prove the existence of a unique solution of the Oberbeck-Boussinesq equations, which describes nonstationary motion of incompressible, heat conducting fluid with a solute. They consider it in the exterior of a three-dimensional sphere. Then they prove some properties about the asymptotic behaviour as t tends to infinity. Namely, they consider the rest state and prove that every solution nearby converges to the rest state if the Rayleigh number and other quantities are small. The present paper improves the asymptotic decay rate of earlier results. The reason for which the authors consider the equation only in the exterior of a sphere seems to be merely that in this case the stationary distributions of the heat and the solute of the rest state can be represented by elementary functions. The paper is well organized. par In order to guarantee the existence of a unique solution and an asymptotic decay rate, the authors assume smallness of Rayleigh number and other quantities. It is not clear to me how stringent their conditions are or how far their Rayleigh number is from the primary bifurcation point.