Freidlin-Wentzell Type Large Deviation Principle for Multi-Scale Locally Monotone SPDEs

TL;DR

This paper establishes a Freidlin-Wentzell type large deviation principle for multi-scale SPDEs using weak convergence and Khasminskii's discretization, applicable to various models without compactness assumptions.

Contribution

It extends large deviation principles to multi-scale SPDEs on unbounded domains without requiring compact embedding assumptions.

Findings

Derived the Laplace principle for a broad class of multi-scale SPDEs.

Applicable to models like stochastic porous media and p-Laplace equations.

Dropped the compactness assumption in the Gelfand triple for unbounded domains.

Abstract

This work is concerned with Freidlin-Wentzell type large deviation principle for a family of multi-scale 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 multi-scale 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 multi-scale SPDE models such as stochastic porous media equations, stochastic p-Laplace equations, stochastic fast-diffusion equations, stochastic 2D hydrodynamical type models, stochastic power law fluid equations and stochastic Ladyzhenskaya models.