Non-relativistic limit analysis of the Chandrasekhar-Thorne relativistic Euler equations with physical vacuum

Our results provide a first step to make rigorous the formal analysis in terms of \(\frac{1}{c^2}\) proposed by Chandrasekhar \cite{Chandra65b}, \cite{Chandra65a}, motivated by the methods of Einstein, Infeld and Hoffmann, see Thorne \cite{Thorne1}. We consider the non-relativistic limit for the loc...

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Bibliographic Details
Published in:arXiv.org 2018-08
Main Authors: Hai-Liang, Li, La-Su, Mai, Marcati, Pierangelo
Format: Article
Language:English
Subjects:
Boundary value problems
Compressibility
Economic models
Euler-Lagrange equation
Eulers equations
Flux density
Free boundaries
Limit analysis
Mathematical analysis
Relativism
Relativistic effects
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Summary:Our results provide a first step to make rigorous the formal analysis in terms of \(\frac{1}{c^2}\) proposed by Chandrasekhar \cite{Chandra65b}, \cite{Chandra65a}, motivated by the methods of Einstein, Infeld and Hoffmann, see Thorne \cite{Thorne1}. We consider the non-relativistic limit for the local smooth solutions to the free boundary value problem of the cylindrically symmetric relativistic Euler equations, when the mass energy density includes the vacuum states at the free boundary. For large enough (rescaled) speed of light \(c\) and suitably small time \(T,\) we obtain uniform, with respect to \(c,\) \lq\lq a priori\rq\rq estimates for the local smooth solutions. Moreover, the smooth solutions of the cylindrically symmetric relativistic Euler equations converge to the solutions of the classical compressible Euler equation, at the rate of order \(\frac{1}{c^2}\).
ISSN:2331-8422