  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.
