学术报告会：Critical thresholds in Euler-Poisson systems with spherical symmetry

报告题目：Critical thresholds in Euler-Poisson systems with spherical symmetry

报  告  人：刘海亮   爱荷华州立大学教授

报告时间：2023年7月18日周二上午10：00

报告地点：S3-313

摘要: The Euler-Poisson system describes the dynamic behavior of many important physical flows including charge transport, plasma with collision and cosmological waves. We prove sharp threshold conditions for the global existence/finite-time- breakdown of solutions to the multidimensional pressureless Euler-Poisson (EP) system with or without background and general initial data. In particular, the initial data could include points where velocity is negative, that is, the flow is directed towards the origin. Obtaining threshold conditions for such systems is extremely hard due to the coupling of various local/nonlocal forces. Remarkably, we are able to achieve a sharp threshold for the zero background case and most importantly, the positive background case, which is quite delicate due to the oscillations present in the solutions. We discover a completely novel nonlinear quantity that helps to analyze the system. In the case of positive back- ground, if the initial data results in a global-in-time solution, then we show that the density is periodic along any single characteristic path. We use the Floquet Theorem to prove periodicity. This is a joint work with Manas BHATNAGAR.

个人简介：

刘海亮，美国爱荷华州立大学数学与计算科学系教授。河南师范大学数学学士学位，清华大学数学硕士学位，中国科学院数学博士学位。主要研究方向为偏微分方程分析，发展解决偏微分方程问题的高阶数值算法及应用等。曾获得多项荣誉和奖项，包括德国洪堡学者，应用数学首席教授（Holl Chair）。最近的工作集中在研究数据驱动的深度学习问题。