一、报告题目：Well-posedness beyond Yudovich and mixed-norm ill-posedness for
Vlasov-Poisson
二、报告人：Quoc-Hung Nguyen(阮国兴) 副研究员
三、时 间：2026年10月13日(周二) 上午 10: 00-11: 00
四、地 点：A4-305
报告摘要： I will discuss two aspects of the low-regularity Cauchy theory for the Vlasov-Poisson equation on the whole space, for both attractive and repulsive interactions. First, in dimensions $d\geq2$, I will present a local well-posedness result for nonnegative finite-mass data whose weighted velocity envelope and a weighted Hölder modulus of positive order in velocity belong to $L^p_x$ for one fixed $p>d$. No spatial differentiability is assumed. This class includes initial densities outside the usual Yudovich-type classes: they may fail to belong even locally to $L^q$ for sufficiently large q. The proof uses nonlinear mixing to transfer velocity regularity to the density and obtain an integrable Lipschitz bound for the self-consistent field. Second, in dimensions one through three, I will show that the classical solution map is discontinuous at the vacuum in $L^p_xL^\infty_v$for every $1\leqp<\infty$. Smooth packets with vanishing mass and initial mixed norm generate an order-one velocity envelope at arbitrarily small times, and at each sufficiently small fixed positive time. These results highlight the role of topology: the local theory gives continuous dependence in phase-space $L^1\capL^p$, while the mixed norm detects instability. The ill-posedness result is joint work with Ke Chen, In-Jee Jeong and Sangwook Tae.
报告人简介：Prof. Nguyen got his Ph.D. in 2014 at the University of Tours. After that, he spent five years for three postdocs in EPFL-Lausanne, SNS-Pisa, and New York University-Abu Dhabi. In 2019, he moved to Shanghai Tech. University, China as an assistant professor. Now, he is at the Chinese Academy of Sciences as an associate professor. He works in various directions: regularity theory for quasilinear elliptic and parabolic equations, nonlinear potential theory, Diperna Lions theory for Transport equation, and free boundary problem in fluid (exactly Muskat problem and Peskin), Mean-field limit. He published his work in some good journals such as CPAM, JEMS, MAMS, AiM, ARMA, CMP, Annals of PDE, JMPA.
欢迎广大师生参加！ 联系人：数学与交叉科学研究院 陈辉
