Uniqueness and decay results for a Boussinesquian nanofluid

In this paper a uniqueness theorem for classical solutions is proved in the case of the evolution of a nanofluid filling a bounded domain under the Boussinesq approximation. The mass density of the nanofluid depends on the temperature and on the nanoparticle volume fraction. A decay in time of a suitable energy is achieved assuming that the material parameters satisfy some conditions. These results are then generalized in the presence of a magnetic field.