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8月11日 8：00-12：00
报告地点：应用数学中心3402
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.
报告人介绍：朱圣国，男，上海交通大学数学科学学院教授、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、英国牛津大学做博士后。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。目前已在国际学术期刊上发表学术论文30余篇，其中包括Transactions of the AMS、Advances in Mathematics、Arch. Ration. Mech. Anal.、Ann. Inst. H. Poincare Anal. Non Lineaire、J. Math. Pures Appl. 等本领域权威杂志。 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。 目前主持科技部国家重点研发计划青年科学家、基金委青年和面上项目各一项。
