On the Small Time Asymptotics of the Three Dimensional Stochastic Planetary Geostrophic Equations of Large‐Scale Ocean Circulation

ABSTRACT The main objective of this paper is to consider a small time large deviation principle for the three dimensional stochastic planetary geostrophic equations of large‐scale ocean circulation driven by multiplicative noise, which involves not only the study of small noise, but also the investigation of the effect of the small, but highly nonlinear term. To obtain the small time large deviation principle, we will show that the probability that the solution stays outside an energy ball is exponentially small so that we can restrict the solution to a sufficiently large energy ball, the main idea is similar as in [15,21].