Freidlin--Wentzell Type Large Deviation Principle for Multiscale Locally Monotone SPDEs
Wei Hong, Shihu Li, Wei Liu · SIAM Journal on Mathematical Analysis · 2021
This work is concerned with a Freidlin--Wentzell type large deviation principle for a family of multiscale quasilinear and semilinear stochastic partial differential equations. Employing the weak convergence method and Khasminskii's time discretization approach, the Laplace principle (equivalently, large deviation principle) for a general class of multiscale SPDEs is derived. In particular, we succeed in dropping the compactness assumption of embedding in the Gelfand triple in order to deal with the case of bounded and unbounded domains in applications. Our main results are applicable to various multiscale SPDE models such as stochastic porous media equations, stochastic $p$-Laplace equations, stochastic fast-diffusion equations, stochastic two-dimensional hydrodynamical type models, stochastic power law fluid equations, and stochastic Ladyzhenskaya models.