  This paper is devoted to proving the strong averaging principle for slow-fast
stochastic partial differential equations with locally monotone coefficients,
where the slow component is a stochastic partial differential equations with
locally monotone coefficients and the fast component is a stochastic partial
differential equations (SPDEs) with strongly monotone coefficients. The result
is applicable to a large class of examples, such as the stochastic porous
medium equation, the stochastic $p$-Laplace equation, the stochastic Burgers
type equation and the stochastic 2D Navier-Stokes equation, which are the
nonlinear stochastic partial differential equations. The main techniques are
based on time discretization and the variational approach to SPDEs.
