報告人：朱圣國 副教授
報告題目：Global classical solutions of the multi-dimensional degenerate compressible Navier-Stoke equations with large data of spherical symmetry
報告時間：2026年5月5日（周二）下午14：00
報告地點：騰訊會議：439678934
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
朱圣國，男，上海交通大學數學科學學院副教授、博導。2015年于上海交通大學獲理學博士學位。畢業之后先后在香港中文大學、澳大利亞莫納什大學、英國牛津大學博士后。2020年返回上海交大任教。主要從事與流體力學及相對論相關的非線性偏微分方程的理論研究工作，在可壓縮Navier-Stokes及Euler方程組的適定性和奇異性方面取得了系統性的研究進展。并于2017年入選英國皇家學會“Newton International Fellow”; 2019年入選中組部國家海外高層次人才引進計劃（青年項目）；2020年入選上海市海外高層次人才引進計劃。
報告摘要：
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.