Turning point principle for the stability of viscous gaseous stars

主讲人：林治武 美国佐治亚理工学院教授

时间：2024年5月9日10：30

地点：三号楼332会议室

举办单位：数理学院

主讲人介绍：林治武，美国布朗大学博士，现为美国佐治亚理工学院教授，从事流体力学、等离子体及非线性波的偏微分方程模型的研究工作，在解的稳定性、解的长时间动力学行为等方面作出一系列有影响的工作。研究成果发表在《Invent.Math.》《Comm. Pure Appl. Math.》《Mem. Amer. Math. Soc.》《Comm. Math. Phys.》《Arch. Ration.Mech. Anal.》等国际著名SCI数学期刊上。现担任《SIAM. J. Math. Anal.》等杂志的编委。

内容介绍：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 Yucong Wang and Ming Cheng.