Stability of the Stokes Immersed Boundary Problem with Bending and Stretching Energy.
Stability of the Stokes Immersed Boundary Problem with Bending and Stretching Energy.
复制标题
具有弯曲和拉伸能量的斯托克斯浸入边界问题的稳定性。
DOI：
10.1016/j.jfa.2021.109204
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Hui Li
中科院分区：
文献类型：
--
作者：
Hui Li
研究了二维Stokes流中具有弯曲能和拉伸能的一维闭合弹性弦的运动。本文引入曲线的切角函数和拉伸函数来描述弹性弦的不同变形。这两个函数分别定义在弧长坐标和材料坐标上。借助于Stokes方程的基本解，我们将问题转化为一个抛物型方程组，称之为轮廓动力系统。在非自相交和良好拉伸的初始构型假设下，我们建立了Sobolev空间中自由边界问题的局部适定性。当初始构型足够接近平衡态（即均匀参数化圆）时，我们证明了解可以整体扩张，并且整体解将随着t→+∞指数收敛到平衡态.
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 (ie 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→+∞.
不可压缩牛顿流体与 Koiter 型壳相互作用的弱解
影响因子：
2.5
作者：
Lengeler;Růžička
通讯作者：
Růžička