再看星系动力学中的Kurth解
A second look at the Kurth solution in galactic dynamics
摘要：
Kurth解是引力Vlasov-Poisson系统的一种特殊的非各向同性定态解。它具有这样的性质，即通过适当的时间相关变换，它可以变成一族时间相关解。因此，对于一般的稳态$Q(x, v)=\tilde{Q}(e_Q, β)$，取决于粒子能量$e_Q$和$β=\ell^2=|x\wedge v|^2$，问题是，对于合适的函数$R$、$P$和$B$，是否可以生成形式为\[ f(t)=\tilde{Q}\Big(e_Q(R(t), P(t), B(t)), B(t)\Big) \]的解$f$，对于$r=|x|$和$p_r=\frac{x\cdot v}{|x|}$，所有这些都取决于$(t, r, p_r, β)$。我们将证明，在一些温和的假设下，基本上如果$R$和$P$独立于$β$，并且如果$B=β$是常数，则$Q$已经是Kurth解。这篇论文是为了纪念罗伯特·伯尔西教授而写的。
英文摘要：
The Kurth solution is a particular non-isotropic steady state solution to the gravitational Vlasov-Poisson system. It has the property that by means of a suitable time-dependent transformation it can be turned into a family of time-dependent solutions. Therefore, for a general steady state $Q(x, v)=\tilde{Q}(e_Q, β)$, depending upon the particle energy $e_Q$ and $β=\ell^2=|x\wedge v|^2$, the question arises if solutions $f$ could be generated that are of the form \[ f(t)=\tilde{Q}\Big(e_Q(R(t), P(t), B(t)), B(t)\Big) \] for suitable functions $R$, $P$ and $B$, all depending on $(t, r, p_r, β)$ for $r=|x|$ and $p_r=\frac{x\cdot v}{|x|}$. We are going to show that, under some mild assumptions, basically if $R$ and $P$ are independent of $β$, and if $B=β$ is constant, then $Q$ already has to be the Kurth solution. This paper is dedicated to the memory of Professor Robert Glassey.
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。
