Abstract
For self-gravitating, spherically symmetric and isentropic gas surrounding a solid star, when the adiabatic index γ ∈ [4/3, 2) we prove that there is a unique equilibrium for given momentum and total mass. When γ ∈ (1, 4/3), we prove that there are multiple equilibria for a certain range of momentum and total mass and the number of equilibria may grow arbitrarily larger for certain γ. These results are consistent with the beliefs of astrophisicists; the stationary solutions are stable if γ > 4/3 and unstable if γ < 4/3. The problems were studied through the classical Lane-Emden equation.
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Work partially supported by the National Science Council of the Republic of China.
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Kuan, Wc., Lin, Ss. Numbers of equilibria for the equation of self-gravitating isentropic gas surrounding a solid ball. Japan J. Indust. Appl. Math. 13, 311–331 (1996). https://doi.org/10.1007/BF03167250
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DOI: https://doi.org/10.1007/BF03167250