Quantitative convergence in relative entropy for a moderately interacting particle system on $\R^d$-陈丽 教授 (德国曼海姆大学)
题目:Quantitative convergence in relative entropy for a moderately interacting particle system on $\R^d$
报告人：陈丽 教授 (德国曼海姆大学)
In this talk, I will show how to combine the relative entropy method introduced by Jabin and Wang and the regularized $L^2(\R^d)$-estimate given by Oeschläger to prove a strong propagation of chaos result for the viscous porous medium equation from a moderately interacting particle system in $L^\infty(0,T; L^1(\R^d))$-norm. In the moderate interacting setting, the interacting potential is a smoothed Dirac Delta distribution, however, current results regarding the relative entropy methods for singular potentials do not apply. The result holds on $\R^d$ for any dimension $d\geq 1$ and provides a quantitative result where the rate of convergence depends on the moderate scaling parameter and the dimension $d\geq 1$. This is a joint work with Alexandra Holzinger and Xiaokai Huo.