不可压缩流体的自由边值问题及其在牛顿力学框架下两体运动中的应用

经典力学中的两体问题历来是数学家和物理学家最感兴趣的问题之一。申请人与合作者通过研究以不可压缩流体自由边值问题为模型的两体运动，证明了当两个星体重心距离达到最小值时，星体自由边界的形变能够改变星体重心轨道的定性行为。在本项目中，申请人打算继续研究当两个星体重心跨过最小距离时刻之后的演化行为，从而最终证明两体运动中的“潮汐俘获”现象能够发生。实现这一目标的一个重要步骤是：证明单个星体自由边值问题小初值解的长时间存在性。

The two-body problem in classical mechanics has been one of the problems which interests mathematicians and physicists most. The applicant and his collaborators studied the two-body problem modeled by a free boundary problem for incompressible fluids, and proved that when the distance of the center of masses of the two bodies reaches its first minimum, a qualitative change of the motion orbit occurs due to the deformation of the free boundaries. In this project, the applicant intends to study the evolution of the two-body motion beyond the minimum distance, and finally prove that the "tidal capture" will happen. A key step to achieve this goal is to prove the long time existence of the free boundary problem with small initial data.