报告人：朱圣国 副教授
报告题目：Global classical solutions of the multi-dimensional degenerate compressible Navier-Stoke equations with large data of spherical symmetry
报告时间：2026年5月5日（周二）下午14：00
报告地点：腾讯会议：439678934
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
朱圣国，男，上海交通大学数学科学学院副教授、博导。2015年于上海交通大学获理学博士学位。毕业之后先后在香港中文大学、澳大利亚莫纳什大学、英国牛津大学博士后。2020年返回上海交大任教。主要从事与流体力学及相对论相关的非线性偏微分方程的理论研究工作，在可压缩Navier-Stokes及Euler方程组的适定性和奇异性方面取得了系统性的研究进展。并于2017年入选英国皇家学会“Newton International Fellow”; 2019年入选中组部国家海外高层次人才引进计划（青年项目）；2020年入选上海市海外高层次人才引进计划。
报告摘要：
A fundamental open problem in the theory of the compressible Navier-Stokes equations is whether regular spherically symmetric flows can develop singularities, such as cavitation or implosion in finite time. A formidable challenge lies in how the well-known coordinate singularity at the origin can be overcome to control the lower or upper bound of the density. In this paper, we consider viscosity coefficients that are degenerately density-dependent, as in the shallow water equations. We prove that, for general large spherically symmetric initial data with bounded positive density, solutions remain globally regular and do not develop cavitation or implosion in two and three spatial dimensions. Moreover, far-field vacuum is allowed for the initial data under consideration here.
