Global well-posedness and large deviations for 3D stochastic Burgers equations - Jiang-lun Wu (Zeitschrift für angewandte Mathematik und Physik, 2020)
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, towards obtaining the global well-posedness, we derive a priori estimates of the local solution by utilising 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.