Non-relativistic limit analysis of the Chandrasekhar-Thorne relativistic Euler equations with physical vacuum
Non-relativistic limit analysis of the Chandrasekhar-Thorne relativistic Euler equations with physical vacuum
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物理真空条件下 Chandrasekhar-Thorne 相对论欧拉方程的非相对论极限分析
DOI：
10.1142/s0218202519500155
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发表时间：
2019
影响因子：
3.5
通讯作者：
Pierangelo Marcati
中科院分区：
文献类型：
--
作者：
La-Su Mai;Hai-Liang Li;Pierangelo Marcati
我们的研究结果提供了第一步，使严格的形式化分析的条款$\frac{1}{c^2}$提出的Chandra 65 b，Chandra 65 a}，激励的方法，爱因斯坦，Infeld和霍夫曼，见索恩\cite{Thorne 1}。考虑柱对称相对论性Euler方程自由边值问题的局部光滑解的非相对论性极限，当自由边界上的质能密度包含真空态时.对于足够大的（重新缩放）光速$c$和适当小的时间$T，$我们得到均匀的，关于$c，$ \lq\lq先验\rq\rq估计的局部光滑的解决方案。此外，柱对称相对论欧拉方程的光滑解以$\frac{1}{c^2}$的速度收敛到经典可压缩欧拉方程的解.
Our results provide a first step to make rigorous the formal analysis in terms of $\frac{1}{c^2}$ proposed by Chandrasekhar \cite{Chandra65b,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 $\frac{1}{c^2}$.