中科院数学与系统科学研究院
数学研究所
调和分析及其应用研究中心
学术报告
调和分析和偏微分方程研讨班
报告人：Professor Lin Zhiwu（Georgia Institute of Technology）
题 目： Turning point principle for the stability of viscous gaseous stars
时 间：2024.06.12（星期三）16:00-17:00
地 点：S803
摘 要： We consider the stability of the non-rotating viscous gaseous stars modeled by the Navier-Stokes-Poisson system. Under general assumptions on the equation of states, we prove that the number of unstable modes of the linearized Navier-Stokes-Poisson system equals that of the linearized Euler-Poisson system modeling inviscid gaseous stars. In particular, the turning point principle holds for the non-rotating stars with viscosity. That is, the stability of the stars is determined by the mass-radius curve parameterized by the center density. The transition of stability only occurs at the extrema of the total mass. For the proof, we establish an infinite-dimensional Kelvin-Tait-Chetaev Theorem for a class of abstract second-order linear equations with dissipation. Moreover, we prove that linear stability implies nonlinear asymptotic stability and linear instability implies nonlinear instability for the Navier-Stokes-Poisson system under spherically symmetric perturbations. This is a joint work with Ming Cheng and Yucong Wang.
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