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April 2015 On spherically symmetric motions of a gaseous star governed by the Euler--Poisson equations
Tetu Makino
Osaka J. Math. 52(2): 545-581 (April 2015).

Abstract

We consider spherically symmetric motions of a polytropic gas under the self-gravitation governed by the Euler--Poisson equations. The adiabatic exponent ($=$ the ratio of the specific heats) $\gamma$ is assumed to satisfy $6/5 < \gamma \leq 2$. Then there are equilibria touching the vacuum with finite radii, and the linearized equation around one of the equilibria has time-periodic solutions. To justify the linearization, we should construct true solutions for which this time-periodic solution plus the equilibrium is the first approximation. We solve this problem by the Nash--Moser theorem. The result will realize the so-called physical vacuum boundary. But the present study restricts $\gamma$ to the case in which $\gamma/(\gamma-1)$ is an integer. Other cases are reserved to the future as an open problem. The time-local existence of smooth solutions to the Cauchy problems is also discussed.

Citation

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Tetu Makino. "On spherically symmetric motions of a gaseous star governed by the Euler--Poisson equations." Osaka J. Math. 52 (2) 545 - 581, April 2015.

Information

Published: April 2015
First available in Project Euclid: 24 March 2015

zbMATH: 1323.35180
MathSciNet: MR3326626

Subjects:
Primary: 35L05, 35L52, 35L57, 35L70, 76L10

Rights: Copyright © 2015 Osaka University and Osaka City University, Departments of Mathematics

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Vol.52 • No. 2 • April 2015
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