Exponential Ergodicity for Singular Reflecting McKean-Vlasov SDEs

By refining a recent result of Xie and Zhang, we prove the exponential ergodicity under a weighted variation norm for singular SDEs with drift containing a local integrable term and a coercive term. This result is then extended to singular reflecting SDEs as well as singular McKean-Vlasov SDEs with or without reflection. We also present a general result deducing the uniform ergodicity of McKean-Vlasov SDEs from that of classical SDEs. As an application, the $L^1$-exponential convergence is derived for a class of non-symmetric singular granular media equations.