可压缩旋转恒星的存在性与稳定性理论

摘要

旋转是宇宙中的一个普遍现象.从Newton时代开始,许多著名的数学家和物理学家如:Maclaurin,Clairaut,Liouville,Lyapunov,Poincaré等人都对旋转星理论作出过非常重要的贡献.旋转里理论中一令基本的问题就是研究自重力旋转流体相对平衡结构的存在性与稳定性,这个问题至今没有完全解决.本文将尝试对其研究历史作一些综述,给出近年来的一些最新进展,并介绍一些未解决的问题.%Rotation is an universal phenomenon. Since the time of Newton, many distinguished mathematicians and physical scientists such as Maclaurin, Clairaut, Liouville, Lyapunov and Poincare have made great contributions on the theory of rotating stars. A classical problem is to investigate the existence and stability of self-gravitating rotating fluids in a relative equilibrium. In this note we survey some historical and recent results on rotating stars, and mention some unsolved problems on this subject.