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

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Xing Huang, Panpan Ren, Feng-Yu Wang
DOI: 10.48550/arxiv.2602.10841
Cited by: 0

Abstract

We study McKean-Vlasov SDEs with interaction kernels in $\tt W^{-\dd,k},$ the local negative Sobolev space on $\R^d$ with indexes $\dd \in [0,\infty)$ and $k\in [1,\infty].$ We derive the local well-posedness for any singular indexes $(\dd,k)\in [0,\infty)\times [1,\infty],$ and prove the global well-posedness for any initial distributions provided $\dd+\ff d k

Fields of Study & Subjects

Stochastic processes and financial applications Geometric Analysis and Curvature Flows Stochastic processes and statistical mechanics

Publication details

Journal / source
arXiv (Cornell University)
Publication date
11 February 2026
Language
EN
Document type
Preprint