Global well-posedness and large deviations for 3D stochastic Burgers equations

In this paper, we study the stochastic vector-valued Burgers equations with non-periodic boundary conditions. We first apply a contraction principle argument to show local existence and uniqueness of a mild solution to this model. Then, toward obtaining the global well-posedness, we derive a priori estimates of the local solution by utilizing the maximum principle. Finally, we establish, by means of the weak convergence approach, the Freidlin–Wentzell type large deviation principle for 3D stochastic Burgers equations when the noise term goes to zero.