Large deviation principle for multi-scale fully local monotone stochastic dynamical systems with multiplicative noise

This paper is devoted to proving the small noise asymptotic behavior, particularly large deviation principle, for multi-scale stochastic dynamical systems with fully local monotone coefficients driven by multiplicative noise. The main techniques rely on the weak convergence approach, the theory of pseudo-monotone operators and the time discretization scheme. The main results derived in this paper have broad applications to various multi-scale models, where the slow component could be such as stochastic porous medium equations, stochastic Cahn-Hilliard equations and stochastic 2D Liquid crystal equations.