广州数学大讲坛第三期

第二十二讲——杭州师范大学尹思露副教授学术报告

题目：On the low-regularity ill-posedness of non-strictly hyperbolic systems

时间：4月3日（周五）上午10：00——11：00

地点：理学实验楼312

报告人：尹思露 副教授

摘要：In this talk, we investigate the ill-posedness of several non-strictly hyperbolic systems characterized by multiple propagation speeds, encompassing elastodynamic waves, the compressible ideal MHD system, and Euler equations. For scalar quasilinear wave equation, Smith-Tataru established local well-posedness in , where the regularity threshold is defined as  for  and  for . Here, we construct explicit counterexamples to demonstrate the failure of local existence for low-regularity solutions to the aforementioned physical systems at the critical borderline regularity. Our proof is based on a coalition of a carefully designed algebraic approach with Christodoulou’s geometric approach. We give a detailed description of solution dynamics up to the earliest singular event, when a shock forms. This talk is based on joint works with Xinliang An (NUS) and Haoyang Chen (NKU).

报告人简介：

尹思露，杭州师范大学副教授，2016年博士毕业于复旦大学，师从周忆教授。主要研究双曲型方程组解的适定性和奇性理论，相关研究成果发表于Memoirs of the AMS、Amer. J. Math.、Comm. Math. Phys.、SIAM J. Math. Anal.等杂志(含接受发表)，荣获2018年上海市青年科技英才扬帆计划、2025年浙江省数学会科研成果二等奖。