  We establish the existence and uniqueness of local strong pathwise solutions
to the stochastic Boussinesq equations with partial diffusion term forced by
multiplicative noise on the torus in $\mathbb{R}^{d},d=2,3$. The solution is
strong in both PDE and probabilistic sense.In the two dimensional case, we
prove the global existence of strong solutions to the Boussinesq equations
forced by additive noise using a suitable stochastic analogue of a logarithmic
Gronwall's lemma. After the global existence and uniqueness of strong solutions
are established, the large deviation principle (LDP) is proved by the weak
convergence method. The weak convergence is shown by a tightness argument in
the appropriate functional space.

Analysis of PDEs