  We give a direct proof of the fact that the $L^{p)$-norms of global solutions
of the Boussinesq system in $R^{3}$ grow large as $ t \rightarrow + \infty $
for $ 1 < p < 3 $ and decay to zero for $ 3 < p \leq \infty $, providing exact
estimates from below and above using a suitable decomposition of the space-time
space $ R^{+} \times R^{3} $. In particular, the kinetic energy blows up as $
\| u(t) \|_{2}^{2} \sim c t^{1/2} $ for large time. This contrasts with the
case of the Navier-Stokes equations.
