# Separable Hamiltonian PDEs and Turning point principle for stability of gaseous stars

@article{Lin2020SeparableHP, title={Separable Hamiltonian PDEs and Turning point principle for stability of gaseous stars}, author={Zhiwu Lin and C. Zeng}, journal={arXiv: Analysis of PDEs}, year={2020} }

We consider stability of non-rotating gaseous stars modeled by the Euler-Poisson system. Under general assumptions on the equation of states, we proved a turning point principle (TPP) that the stability of the stars is entirely determined by the mass-radius curve parameterized by the center density. In particular, the stability can only change at extrema (i.e. local maximum or minimum points) of the total mass. For very general equation of states, TPP implies that for increasing center density… Expand

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