Lane-Emden星、自引力盘和Sobolev不等式
Lane-Emden stars, selfgravitating disks and the Sobolev inequality
摘要：
利用著名的Sobolev不等式估计了自引力多方盘的最小质量。这个界限类似于众所周知的Lane-Emden恒星的质量公式。对于多变指数n = 3的理想气体，最小质量不小于金斯质量.在一些数值例子中验证了估计的准确性。这种束缚对于重的自引力盘很有效，而对于轻的盘就不那么有用了。
英文摘要：
We estimate the minimal mass of selfgravitating polytropic disks using the famous Sobolev inequality. This bound resembles the well known mass formula for Lane-Emden stars. For ideal gas with the polytropic index n = 3 the minimal mass is not smaller than the Jeans mass. The accuracy of the estimate is verified in a number of numerical examples. The bound works well for heavy selfgravitating disks and is less useful for light disks.
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。
