Quantitative Propagation of Chaos in $L^{\eta }(\eta \in (0,1])$-Wasserstein distance for Mean Field Interacting Particle System

In this paper, quantitative propagation of chaos in $L^{\eta }$($\eta \in (0,1]$)-Wasserstein distance for mean field interacting particle system is derived, where the diffusion coefficient is allowed to be interacting and the initial distribution of interacting particle system converges to that of the limit equation in $L^1$-Wasserstein distance. The non-degenerate and second order system are investigated respectively and the main tool relies on the gradient estimate of the decoupled SDEs.