Averaging Principle for Multi-Scale McKean-Vlasov SPDEs with Locally Monotone Coefficients

In this paper we establish the strong averaging principle for a class of multi-scale McKean-Vlasov stochastic partial differential equations with locally monotone coefficients. Using the techniques of time discretization and stopping time, we prove that the slow component converges to the solution of the averaged equation. The main results are applicable to a large class of multi-scale McKean-Vlasov SPDE models such as multi-scale stochastic porous media equations, stochastic p-Laplace equations, stochastic 2D Navier-Stokes equations, stochastic Burgers type equations, stochastic power law fluid equations and stochastic Ladyzhenskaya equations.