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 medium 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.

中文翻译：

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具有局部单调系数的SPDE的小时间渐近性

这项工作旨在证明广义变分框架中一类具有局部单调系数的随机偏微分方程（SPDE）的小时间大偏差原理（LDP）。主要结果可用于证明各种准线性和半线性SPDE的小时间LDP，例如随机多孔介质方程，随机$ p $ -Laplace方程，随机Burgers型方程，随机2D Navier-Stokes方程，随机幂律流体方程和随机Ladyzhenskaya模型。特别是，对于具有乘性噪声的一般准线性SPDE，我们的小时间LDP结果似乎是新的。