Stability of the Stokes immersed boundary problem with bending and stretching energy
报告题目(Title)：Stability of the Stokes immersed boundary problem with bending and stretching energy
报告人(Speaker)：李徽 博士 （浙江大学）
地点(Place)：腾讯会议 ID：397 173 154会议密码：123456
时间(Time)：2021-06-17（星期四）， 2:00-3:00 pm （Beijing Time）
邀请人(Inviter)：许孝精, 袁迪凡
报告摘要
In this talk, we show stability results of hydrodynamics on the moving surface of an elastic string with bending and stretching energy immersed in a 2-D Stokes flow. We introduce the curve’s tangent angle function and the stretching function to describe the deferent deformations of the elastic string. These two functions are defined on the arc-length coordinate and the material coordinate respectively. With the help of the fundamental solution of the Stokes equation, we reformulate the problem into a parabolic system which is called the contour dynamic system. Under the non-self-intersecting and well-stretched assumptions on initial configurations, we establish the local well-posedness of the free boundary problem in Sobolev space. When the initial configurations are sufficiently close to the equilibrium state (i.e. an evenly parametrized circle), we prove that the solutions can be extended globally and the global solutions will converge to the equilibrium state exponentially as t $\to +\infty$.
