重新审视非旋转恒星模型：经典存在性和唯一性理论及尺度关系
Revisiting Non-Rotating Star Models: Classical Existence and Uniqueness Theory and Scaling Relations
AI总结：
本文研究非旋转恒星模型在一般状态方程下的性质，扩展了Auchmuty和Beals的存在性结果，并将Lieb和Yau的量子力学唯一性结果应用于经典牛顿力学框架，同时通过尺度方法建立不同总质量解之间的关系。
摘要：
本文系统研究了由欧拉-泊松系统支配的非旋转恒星模型的性质，包括多聚体气体恒星的情况。我们重新审视并扩展了Auchmuty和Beals的结果，将Lieb和Yau的量子力学框架中的唯一性结果适应到经典牛顿力学设定中。这些结果也综合在McCann的文献中，但未附证明。第二项工作是应用尺度方法，建立不同总质量解之间的关系。当质量趋于零时，我们分析密度函数的收敛性质，并确定其支持域收缩或扩展的精确速率。
英文摘要：
This paper presents a systematic study of the properties of non-rotating stellar models governed by the Euler-Poisson system under general equations of state, including the case of polytropic gaseous stars. We revisit and extend existence results by Auchmuty and Beals \cite{AB71}, adapt the uniqueness results from the quantum mechanical framework of Lieb and Yau \cite{LY87} to the classical Newtonian mechanical setting. The results are also synthesized in McCann \cite{McC06} but without proof. The second work we do is applying a scaling method to establish relations between solutions with different total masses. As the mass tends to zero, we analyze convergence properties of the density functions and identify precise rates for the contraction or extension of their supports.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
