应304am永利集团官网王跃循教授和崔秀芳副教授邀请，上海交通大学数学科学学院朱圣国副教授将于2023年11月11日上午举办学术报告。
报告题目:Formation of singularities for the relativistic Euler equations
时 间：11月11日（星期六）09：45-10: 30
地 点：理工楼518
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, on the one hand, for the C1 solutions with large data and possible far field vacuum to the isentropic flow, we verified the theory obtained by P. D. Lax in 1964. On the other hand, for the C1 solutions with large data and strictly positive initial mass-energy density to the non-isentropic flow, we exhibit a numerical value N, thought of as representing the strength of an initial compression, above which all initial data lead to a finite-time singularity formation. These singularities manifest as a blow-up in the gradient of certain Riemann invariants associated with corresponding systems.This talk is mainly based on joint works with Dr. Tianrui Bayles-Rea (Oxford) and Dr. Nikolaos Athanasiou (Oxford).
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报告人简介
朱圣国，上海交通大学副教授，博士生导师。2015年博士毕业于上海交通大学，2015年至2020年先后在香港中文大学、澳大利亚莫纳什大学（Monash University）、英国牛津大学（University of Oxford）做博士后，并于2017年入选英国皇家学会”Newton International Fellow”，2020年至今在上海交通大学数学科学学院工作，国家人才计划青年项目入选者。主要从事流体力学和相对论中的偏微分方程的理论研究，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重要进展，目前已在 “Trans. Amer. Math. Soc.”、“Adv. Math.”、“Arch. Ration. Mech. Anal.”、“Ann. Inst. H. Poincare Anal. Non Lineaire” “J. Math. Pures Appl.”等国际学术期刊上发表论文多篇。
甘肃应用数学中心
甘肃省高校应用数学与复杂系统省级重点实验室
304am永利集团官网
萃英学院
2023年11月9日
