科学研究

学术交流

首页 >  科学研究 >  学术交流 >  正文
The N-Vortex Problem, periodic solutions,and symplectic capacity
作者:    时间:2018-09-17 浏览次数:

  

报告人:王峮 博士

报告时间:9月19日下午3点

报告地点:数学与统计学院一楼报告厅

报告摘要:

The N-vortex problem finds its origin in The vortex dynamics finds its root in hydrodynamics with 160 years of history. In 1858 Hermann von Helmholtz’s seminal paper has marked its birth and then Kirchhoff in 1876 has shown its Hamiltonian structure. It is well known that for N>3 this problem is in general non-integrable, thus the searching of periodic solution serves as an important approach to understand the dynamics.

Many interesting results in this fields are produced through methods developed in celestial mechanics, especially perturbative aspects. On the other hand, in recent years following the figure eight solution of Chenciner and Montgomery, variational methods have been proved to be very efficient in searching for periodic solutions in N-body problem. In this talk I would like to explore the possibility in application of variational methods in the search of periodic solutions for N-vortex Hamiltonian systems with positive vorticities, and resume some basic results obtained through symplectic capacity approach.

 

报告人简介:

教育经历:

2005.9-2009.6 武汉大学 学士

研究方向:

变分法、辛几何、哈密尔顿系统及其在涡旋动力学和天体力学中的应用。已有论文发表在学术期刊Arch. Rational Mech. Anal.上。