论文标题
Stokes浸入边界问题的稳定性，弯曲和拉伸能量
Stability of the Stokes Immersed Boundary Problem with Bending and Stretching Energy
论文作者
论文摘要
我们研究了一条1-D闭合弹性串的运动，并融入了2D Stokes流中的弯曲和拉伸能量。在本文中，我们介绍了曲线的切角函数和拉伸函数，以描述弹性字符串的递延变形。这两个函数分别在弧长坐标和材料坐标上定义。在Stokes方程的基本解决方案的帮助下，我们将问题重新制定为抛物线系统，该系统称为轮廓动态系统。在初始配置的非自我交流且紧张的假设下，我们在Sobolev空间中建立了自由边界问题的局部良好性。当初始配置足够接近平衡状态（即一个均匀的参数化圆）时，我们证明可以在全球扩展解决方案，并且全局溶液将融合到均衡状态，为T $ \ to t $ \ to $ +$ \ $ \ infty $。
We study the motion of a 1-D closed elastic string with bending and stretching energy immersed in a 2-D Stokes flow. In this paper 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 $\to$ +$\infty$.
