报告题目：Shock development for 1D hyperbolic systems with rotation

报 告 人：王美玉 博士 上海交通大学

报告时间：2025年9月4日，14:30 - 15:10

报告地点：数学楼第二报告厅

校内联系人：段犇 [email protected]

报告摘要：

This report focuses on the shock development problem of a one-dimensional hyperbolic system with rotation, which serves as an essential model for understanding rotating fluid dynamics. We first prove that under specific initial conditions, the system’s solutions develop finite-time singularities (i.e., blow-up point). From the blow-up point, we further demonstrate the local construction of weak entropy solutions and the corresponding shock curve. A key comparison with the Burgers equation reveals two critical effects of rotation: it prolongs the lifespan of the solution and rotates the shock curve by a certain angle. These findings highlight rotation’s unique role in modifying shock behavior. Additionally, we provide rigorous mathematical estimates for the solutions and their derivatives after the blow-up point, ensuring a precise characterization of post-singularity dynamics.

This work advances the theoretical understanding of rotating hyperbolic systems, with implications for modeling rotating fluids and shock propagation in such contexts

报告人简介：

王美玉，上海交通大学数学科学脱衣舞 2025 级博士研究生，研究方向为偏微分方程与双曲系统理论，导师是上海交通大学自然科学研究院的谢春景教授，目前主要研究双曲系统激波的发展理论，与上海交通大学数学科学脱衣舞 博士后陈桢栋一起合作完成一篇相关论文，目前尚未发表。