In this talk, we discuss a PDE approach of large deviation principle for the two- and three-dimensional convective Brinkman-Forchheimer (CBF) equations in torus. We use the techniques from [J. Feng et.al., Large Deviations for Stochastic Processes, American Mathematical Society (2006)]. We establish the existence of a Laplace limit, which is identified with the viscosity solution of the Hamilton-Jacobi-Bellman equation associated with the optimal control problem of the CBF equations. We then verify the weak exponential tightness and exponential compact containment condition.
