Formation of singularities for the relativistic Euler equations
数学专题报告
报告题目(Title)：Formation of singularities for the relativistic Euler equations
报告人(Speaker)：朱圣国 副教授（上海交通大学）
地点(Place)：腾讯会议：716652440 密码：168293
时间(Time)：2025年11月29日（周六）9:30-10:30
邀请人(Inviter)：袁迪凡
报告摘要
We consider large data problems for C1 solutions of the relativistic Euler equations. In the (1 + 1)-dimensional spacetime setting, if the initial data are strictly away from the vacuum, a key difficulty in considering the singularity formation is coming up with a way to obtain sharp enough control on the lower bound of the mass-energy density. For this reason, via an elaborate argument on a certain ODE inequality and introducing some key artificial (new) quantities, we provide one time-dependent lower bound of the mass-energy density of the (1+1)-dimensional relativistic Euler equations, which involves looking at the difference of the two Riemann invariants, along with certain weighted gradients of them. Ultimately, for C1 solutions with uniformly positive initial mass-energy density of the corresponding Cauchy problem, we give a necessary and sufficient condition for the singularity formation in finite time. This talk is mainly based on joint works with Nikolaos Athanasiou (ICL).
