Linearized Analysis of Barotropic Perturbations around Spherically Symmetric Gaseous Stars Governed by the Euler-Poisson Equations

Abstract

The hydrodynamic evolution of self-gravitating gaseous stars is governed by the Euler-Poisson equations. We study the structure of the linear approximation of barotropic perturbations around spherically symmetric equilibria based on functional analytic tools. In contrast to folklore, we show that the spectrum of the linearized operator for general perturbations is not of the Sturm-Liouville type unless the perturbations are restricted. In particular, we prove that it is of the Sturm-Liouville type for irrotational perturbations.

arXiv commentFinal revision accepted by Journal of Mathematical Physics

References in corpus (2)

• On Rotating Axisymmetric Solutions of the Euler-Poisson Equations
• On spherically symmetric motions of a gaseous star governed by the Euler-Poisson equations

Cited by in corpus (4)

• Stability of rotating gaseous stars
• Separable Hamiltonian PDEs and Turning point principle for stability of gaseous stars
• On Linear Adiabatic Perturbations of Spherically Symmetric Gaseous Stars Governed by the Euler-Poisson Equations
• On Adiabatic Oscillations of a Stratified Atmosphere on the Flat Earth