應yl7703永利官網(wǎng)王躍循教授和崔秀芳副教授邀請，上海交通大學數(shù)學科學學院朱圣國副教授將于2023年11月11日上午舉辦學術報告。

報告題目:Formation of singularities for the relativistic Euler equations

時 間：11月11日（星期六）09：45-10: 30

地 點：理工樓518

報告摘要：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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報告人簡介

朱圣國，上海交通大學副教授，博士生導師。2015年博士畢業(yè)于上海交通大學，2015年至2020年先后在香港中文大學、澳大利亞莫納什大學（Monash University）、英國牛津大學（University of Oxford）做博士后，并于2017年入選英國皇家學會”Newton International Fellow”，2020年至今在上海交通大學數(shù)學科學學院工作，國家人才計劃青年項目入選者。主要從事流體力學和相對論中的偏微分方程的理論研究，在可壓縮Navier-Stokes及Euler方程組的適定性和奇異性方面取得了一系列重要進展，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.”等國際學術期刊上發(fā)表論文多篇。

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萃英學院

2023年11月9日