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

## TL;DR

This paper proves the existence, uniqueness, and large deviation principles for strong solutions to stochastic Boussinesq equations with partial diffusion, advancing understanding of their probabilistic behavior in 2D and 3D.

## Contribution

It establishes local and global strong pathwise solutions for stochastic Boussinesq equations with partial diffusion, and proves a large deviation principle using weak convergence methods.

## Key findings

- Existence and uniqueness of local strong solutions in 2D and 3D.
- Global strong solutions in 2D with additive noise.
- Large deviation principle established for the solutions.

## Abstract

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.