Well-posedness and averaging principle of McKean-Vlasov SPDEs driven by cylindrical $α$-stable process

Abstract: In this paper, we first study the well-posedness of a class of McKean-Vlasov stochastic partial differential equations driven by cylindrical $\alpha$-stable process, where $\alpha\in(1,2)$. Then by the method of the Khasminskii's time discretization, we prove the averaging principle of a class of multiscale McKean-Vlasov stochastic partial differential equations driven by cylindrical $\alpha$-stable processes. Meanwhile, we obtain a specific strong convergence rate.