Turning point principle for the stability of viscous gaseous stars

主講人：林治武 美國(guó)佐治亞理工學(xué)院教授

時(shí)間：2024年5月9日10：30

地點(diǎn)：三號(hào)樓332會(huì)議室

舉辦單位：數(shù)理學(xué)院

主講人介紹：林治武，美國(guó)布朗大學(xué)博士，現(xiàn)為美國(guó)佐治亞理工學(xué)院教授，從事流體力學(xué)、等離子體及非線(xiàn)性波的偏微分方程模型的研究工作，在解的穩(wěn)定性、解的長(zhǎng)時(shí)間動(dòng)力學(xué)行為等方面作出一系列有影響的工作。研究成果發(fā)表在《Invent.Math.》《Comm. Pure Appl. Math.》《Mem. Amer. Math. Soc.》《Comm. Math. Phys.》《Arch. Ration.Mech. Anal.》等國(guó)際著名SCI數(shù)學(xué)期刊上。現(xiàn)擔(dān)任《SIAM. J. Math. Anal.》等雜志的編委。

內(nèi)容介紹：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.