报告题目：Expanding solutions near unstable Lane-Emden stars
时 间：2024-06-26 (星期三) 10:00
地 点：科研楼18号楼1102
主 办：数学与统计学院、分析数学及应用教育部重点实验室、福建省分析数学及应用重点实验室、统计学与人工智能福建省高校重点实验室、福建省应用数学中心（福建师范大学）
参加对象：感兴趣的老师和研究生
报告摘要：We consider the compressible Euler-Poisson equations for polytropes and the white dwarf stars. For polytropic index 4/3, we show that there is a global weak solution for the spherically symmetric initial data with mass less than the critical mass of the Lane-Emden stars (i.e. nonrotating polytropes). For polytropic index in (6/5,4/3), we show the existence of global weak solution for spherical symmetric initial data in an invariant set containing a neighborhood of Lane-Emden stars. Moreover, the support of both solutions expands to infinity as time goes to plus or minus infinity. As a corollary, this proves the strong instability of the Lane-Emden stars for polytropic index in (6/5,4/3). For for polytropic index in (6/5,4/3), our results provide the first example of expanding solutions. For white dwarf stars, we prove that the solution cannot collapse if the mass of initial data is less than the Chandrasekhar limit mass, which is the supremum of the mass of the non-rotating white dwarf stars. Our proof strongly uses the variational characterization of Lane-Emden stars. First, we relate the best constant of a Hardy-Littlewood type inequality with the mass of the Lane-Emden stars with polytropic index 4/3, which is further shown to equal the Chandrasekhar limit mass. For polytropic index in (6/5,4/3), a crucial ingredient in the the construction of the invariant set of expanding solutions is to show that the Lane-Emden stars are minimizers of energy-mass functional subject to a Pohozaev type constraint. This is a joint work with Ming Chang and Xing Cheng.
报告人简介：林治武，美国布朗大学博士，乔治亚理工学院教授。从事偏微分方程，动力系统及其应用领域的研究工作，在解的稳定性、长时间行为等方面作出一系列开创性的工作，研究成果发表在Invent Math、Memoirs of AMS、CPAM等国际期刊上。担任SIAM. J. Math. Anal.等杂志编委。近几年代表性成果包括：线性哈密尔顿偏微分方程的稳定性的一般理论；证明旋转和非旋转星体稳定性的拐点原理（turning point principle)；证明Stuart 1965年关于Kelvin-Stuart 涡旋解的稳定性和不稳定性的猜想等。