Global existence of Lagrangian solutions to the ionic Vlasov--Poisson system
数学专题报告
报告题目(Title)：Global existence of Lagrangian solutions to the ionic Vlasov--Poisson system
报告人(Speaker)：Dowan Koo (Yonsei University)
地点(Place)：Zoom ID: 825 586 45795 会议密码: 964925
时间(Time)：2025年5月3日 （周六） 16:00-17:00
邀请人(Inviter)：袁迪凡
报告摘要
In this talk, we study the Cauchy problem for the ionic Vlasov--Poisson(iVP) system under mild integrability assumptions on the initial data. To this end, we establish the well-posedness of the nonlinear elliptic equation in the iVP system, known as the Poisson--Boltzmann equation, by introducing a novel decomposition of the equation to exploit the method of Calculus of Variations more effectively. This analysis covers $L^p$ densities for any $p>1$, which improves the previously investigated range $p>\frac{d}{2}$ for dimensions $d\ge2$. We further investigate various stability and continuity properties of the solutions to Poisson--Boltzmann equations. As an application, we construct global-in-time Lagrangian solutions in the sense of Ambrosio, Colombo, and Figalli (Duke, 2017) for the ionic Vlasov--Poisson system. This talk is based on a joint work with Young-Pil Choi and Sihyun Song (Yonsei University).
