讲座公告:缪爽:Tidal energy in Newtonian two-body motion
通讯员:  发布人:沈彤  发布时间:2019-10-28   浏览次数:10

讲座时间:20191030号上午10--11

讲座地点:文波四楼统数会议室

讲座题目:Tidal energy in Newtonian two-body motion

讲座摘要In this work, which is based on an essential linear analysis by Christodoulou, we study the tidal energy for the motion of two gravitating incompressible fluid balls with free boundaries, obeying the Euler-Poisson equations. The orbital energy is defined as the mechanical energy of the center of mass of the two bodies. When the fluids are replaced by point masses, according to the classical analysis of Kepler and Newton, the conic curve describing the trajectories of the bodies is a hyperbola when the orbital energy is positive and an ellipse when the orbital energy is negative. If the point masses are initially very far, then the orbital energy, which is conserved in the case of point masses, is positive corresponding to hyperbolic motion. However, in the motion of fluid balls the orbital energy is no longer conserved, as part of the conserved energy is used in deforming the boundaries of the bodies. This energy is called the tidal energy. If the tidal energy becomes larger than the total energy during the evolution, the orbital energy must change its sign, signaling a qualitative change in the orbit of the bodies. We will show that under appropriate conditions on the initial configuration this change of sign occurs. Our analysis relies on an a-priori estimates which we establish up to the point of closest approach. This is a joint work with Sohrab Shahshahani.

主讲人简介缪爽于20137月在中国科学院数学研究所获博士学位,读博期间曾在瑞士苏黎世联邦理工学院学习交流。入选国家青年千人计划,现任武汉大学数学与统计学院教授。入职武大前,曾在美国密歇根大学,瑞士洛桑联邦理工学院从事博士后研究。主要研究以下三个方面的问题:三维拟线性波动方程(可压缩欧拉方程,非线性电磁波等)解的激波形成机制,不可压缩欧拉-泊松方程自由边值问题解的长时间行为,和能量临界波映照方程能量集中爆破解的稳定性。缪教授研究兴趣为双曲型偏微分方程,他出版专著一部,在数学的顶级杂志 Inventiones Mathematicae, Communication in Mathematical Physics 等上发表SCI论文10余篇。