# On the small time asymptotics of 3D stochastic primitive equations

## TL;DR

This paper proves a small time large deviation principle for the strong solutions of 3D stochastic primitive equations with multiplicative noise, accounting for small noise effects and highly nonlinear terms.

## Contribution

It introduces a novel large deviation analysis for 3D stochastic primitive equations considering both small noise and nonlinear unbounded terms.

## Key findings

- Established a small time large deviation principle for the equations.
- Analyzed effects of multiplicative noise on solution behavior.
- Handled highly nonlinear unbounded nonlinear terms.

## Abstract

In this paper, we establish a small time large deviation principle for the strong solution of 3D stochastic primitive equations driven by multiplicative noise. Both the small noise and the small, but highly nonlinear, unbounded nonlinear terms should be taken into consideration.