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

Strong pathwise solution and large deviation principle for the stochastic Boussinesq equations with partial diffusion term