论文标题
弗拉索夫旋转星系模型的全球延续
Global Continuation of a Vlasov Model of Rotating Galaxies
论文作者
论文摘要
一个典型的星系由重力彼此吸引的大量恒星组成。例如，银河系的$ 10^{11} $星星。因此，它通常由Vlasov-Poisson系统建模。我们证明了可能迅速旋转的星系的轴对称稳态的存在定理。此类状态是根据相当通用的粒子能量和角动量的$ ϕ $给出的。此类状态的集合$ \数学k $在适当的功能空间中形成连接的集合。沿着集合的$ \ Mathcal K $，我们在某些条件下证明了（a）星系的支撑是无限的，或者（b）旋转速度和星系中某个地方的密度都没有结合。
A typical galaxy consists of a huge number of stars attracted to each other by gravity. For instance, the Milky Way has about $10^{11}$ stars. Thus it is typically modeled by the Vlasov-Poisson system. We prove an existence theorem for axisymmetric steady states of galaxies that may rotate rapidly. Such states are given in terms of a fairly general function $ϕ$ of the particle energy and angular momentum. The set $\mathcal K$ of such states form a connected set in an appropriate function space. Along the set $\mathcal K$, we prove under some conditions that either (a) the supports of the galaxies become unbounded or (b) both the rotation speeds and the densities somewhere within the galaxy become unbounded.
