Speaker: 郝子墨，北京理工大学

Inviter: 随机分析研究中心

Title: Singular kinetic McKean-Vlasov SDEs: Well-posedness, Quantitative PoC, and Fluctuation- dissipative models

Language: Chinese

Time & Venue: 2026.05.29 16:00-17:00 南楼N613

Abstract: This talk reviews recent progress on singular kinetic McKean–Vlasov stochastic differen- tial equations, with emphasis on well-posedness, quantitative propagation of chaos, and fluctuation– dissipative models. We first discuss how the kinetic structure, combining transport in position and dif- fusion in velocity, provides anisotropic regularization that allows one to treat singular or distributional interaction kernels. This leads to well-posedness results for nonlinear kinetic Fokker–Planck equations and the associated McKean–Vlasov SDEs, including models with Coulomb, Riesz, Biot–Savart, or more general singular interactions.

The second part focuses on quantitative propagation of chaos for interacting particle systems. We compare approaches based on density estimates, martingale arguments, Krylov-type bounds, Girsanov transforms, and relative entropy methods, which yield explicit convergence rates from the N-particle system to the nonlinear mean-field limit.

Finally, we discuss fluctuation–dissipative kinetic models, especially Vlasov–Fokker–Planck–Dean– Kawasaki type equations. These models describe mesoscopic fluctuations around mean-field dynamics and connect singular kinetic McKean–Vlasov theory with stochastic hydrodynamic limits, entropy dissipation, and conservative noise structures.