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娱乐城 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娱乐城博士后陈桢栋一起合作完成一篇相关论文，目前尚未发表。