MR3379135 Tetu MAKINO Tetu MAKINO On Spherically Symmetric Motions of the Atmosphere Surrounding a Planet Governed by the Compressible Euler Equations Funkcialaj Ekvacioj. Serio Internacia 58 2015 43--85 http://fe.math.kobe-u.ac.jp/FE/FullPapers/58-1/58_43.pdf http://www.ams.org/mathscinet-getitem?mr=MR3379135 We consider spherically symmetric motions of inviscid compressible gas surrounding a solid ball under the gravity of the core. Equilibria touch 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. But this leads us to difficulty caused by singularities at the free boundary touching the vacuum. We solve this problem by the Nash-Moser theorem. Compressible Euler equations, Spherically symmetric solutions, Vacuum boundary, Nash-Moser theorem. 35L05, 35L52, 35L57, 35L70, 76L10. 58-43 2015 On Spherically Symmetric Motions of the Atmosphere Surrounding a Planet Governed by the Compressible Euler Equations Tetu MAKINO Tetu MAKINO 1 Adams, R. A. Sobolev Spaces Pure and Applied Mathematics, Vol. 65, Academic Press, New York-London 1975 MR0450957 2 Coddington, E. A.; Levinson, N. Theory of Ordinary Differential Equations McGraw-Hill Book Company, Inc., New York-Toronto-London 1955 MR0069338
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