An application of the Nash-Moser theorem to the vacuum boundary problem of gaseous stars

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• 作者：Tetu Makino¹ ; ^{makino@yamaguchi-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35L70 ; 35Q31 ; 35Q85 ; 76L10 ; 83C05
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：262
• 期：2
• 页码：803-843
• 全文大小：414 K

文摘

We have been studying spherically symmetric motions of gaseous stars with physical vacuum boundary governed either by the Euler–Poisson equations in the non-relativistic theory or by the Einstein–Euler equations in the relativistic theory. The problems are to construct solutions whose first approximations are small time-periodic solutions to the linearized problem at an equilibrium and to construct solutions to the Cauchy problem near an equilibrium. These problems can be solved when 1/(γ−1)$1/(\gamma -1)$ is an integer, where γ   is the adiabatic exponent of the gas near the vacuum, by the formulation by R. Hamilton of the Nash–Moser theorem. We discuss on an application of the formulation by J.T. Schwartz of the Nash–Moser theorem to the case in which 1/(γ−1)$1/(\gamma -1)$ is not an integer but sufficiently large.