McKean-Vlasov SDEs with Local Distributional Interactions: Well-Posedness and Entropy-Cost Estimates

Xing Huang, Panpan Ren, Feng-Yu Wang

We study McKean-Vlasov SDEs with interaction kernels in $\tt W^{-\dd,k},$ the local negative Sobolev space on ${\mathbb{R}}^d$ with indexes $\dd \in [0,\infty)$ and $k\in [1,\infty ].$ We der…