Small Time Asymptotics for SPDEs with Locally Monotone Coefficients

TL;DR

This paper establishes the small time large deviation principle for a broad class of SPDEs with locally monotone coefficients, extending understanding of their probabilistic behavior in the short time regime.

Contribution

It proves the small time LDP for SPDEs with locally monotone coefficients, including new results for quasilinear SPDEs with multiplicative noise.

Findings

Small time LDP established for various SPDEs.

Application to quasilinear and semilinear equations.

New results for quasilinear SPDEs with multiplicative noise.

Abstract

This work aims to prove the small time large deviation principle (LDP) for a class of stochastic partial differential equations (SPDEs) with locally monotone coefficients in generalized variational framework. The main result could be applied to demonstrate the small time LDP for various quasilinear and semilinear SPDEs such as stochastic porous media equations, stochastic $p$-Laplace equations, stochastic Burgers type equation, stochastic 2D Navier-Stokes equation, stochastic power law fluid equation and stochastic Ladyzhenskaya model. In particular, our small time LDP result seems to be new in the case of general quasilinear SPDEs with multiplicative noise.