报告专家：朱圣国副教授（上海交通大学）

报告题目：Formation of singularities for the relativistic Euler equations

报告地点：J9-425

报告时间：7月1日上午10:00-11:00

报告简介：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).

专家个人简介：朱圣国，男，上海交通大学数学科学学院副教授。2015年于上海交通大学获理学博士学位。曾先后在香港中文大学数学科学研究所、澳大利亚莫纳什大学数学学院、英国牛津大学数学研究所做博士后。主要从事与流体力学及相对论相关的非线性偏微分方程的理论研究工作，在可压缩Navier-Stokes 及Euler方程组的适定性和奇异性方面取得了一系列进展。目前已在国际学术期刊上发表学术论文20余篇，其中包括Arch. Ration. Mech. Anal.、Ann. Inst. H. Poincare Anal. Non Lineaire、J. Math. Pures Appl. 等本领域权威杂志。 并于2017年入选英国皇家学会“Newton International Fellow”;  2019年入选中组部国家海外高层次人才引进计划（青年项目）；2020年入选上海市海外高层次人才引进计划。