Algebraic L2 decay for weak solutions of a viscous Boussinesq system in exterior domains

The algebraic decay rates for the total kinetic energy of weak solutions of the n-dimensional viscous Boussinesq system in exterior domains are established by means of the spectral decomposition method of fractional powers of the Laplacian and Stokes operators. The results reveal that L2-decay of the velocity field with zero divergence becomes slower than that of the temperature.