摘要：In this work we establish the local and global well-poseness of weak and strong solutions for second order mean-field SDEs with singular interaction kernels such as Newtonian or Coulomb potential, Riesz potential. Moreover, we also show the smoothness and the short time and long time asymptotic estimate of the density. Our results reveal a phenomenon that for nonlinear mean-field equation, the regularity of the initial density could balance the singularity of the kernel. In particular, our results provide microscopic probability explanation for many physical models including Vlasov-Poisson-Fokker-Planck system, 2d-stochastic vortex system, surface quasi-geostropic models, fractional porous media equation with viscosity. (This is an ongoing work with Zimo Hao.)

个人简介： 北京理工大学数学与统计学院教授。研究方向主要为随机分析及其应用。2013年获国家自然科学基金杰出青年项目资助，2016年获教育部国家高层次人才特聘教授。

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