On spherically symmetric motions of a gaseous star governed by the Euler-Poisson equations

Abstract

We study spherically symmetric motions of a gaseous star governed by the Euler-Poisson equations. Equilibria are given as solutions of the Lane-Emden equations, and the linearized equation around one of these equilibria admits time-periodic solutions. To justify the linearization, we should construct true solutions of the nonlinear evolution equation for which this time-periodic solutions plus the equilibrium is the first approximation. To do so, we apply the Nash-Moser theory. We presents a partial result under some assumptions on the adiabatic exponent of the gas, and propose an open problem to be studied in the future.

arXiv commentTypos corrected and rude expressions revised thanks to suggestions by an anonymous referee. arXiv admin note: text overlap with arXiv:1210.3670

References in corpus (1)

• An Application of Nash-Moser Theorem to Smooth Solutions of One-Dimensional Compressible Euler Equation with Gravity

Cited by in corpus (2)

• Linearized Analysis of Barotropic Perturbations around Spherically Symmetric Gaseous Stars Governed by the Euler-Poisson Equations
• On Adiabatic Oscillations of a Stratified Atmosphere on the Flat Earth