Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We consider the Boussinesq equations in either an exterior domain in R-n, the whole space R-n, the half space R-+(n) or a bounded domain in R-n, where the dimension n satisfies n >= 3. We give a class of stable steady solutions, which improves and complements the previous stability results. Our results give a complete answer to the stability problem for the Boussinesq equations in weak-L-p spaces, in the sense that we only assume that the stable steady solution belongs to scaling invariant class L-sigma((n, infinity)) x L-(n,L- infinity). Moreover, some considerations about the exponential decay (in bounded domains) and the uniqueness of the disturbance are done.93667684Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)