论文标题
Lipschitz班级的全球存在，用于N-Peskin问题
Global existence in the Lipschitz class for the N-Peskin problem
论文作者
论文摘要
在本文中，我们研究了佩斯金问题的玩具模型，该模型捕获了正常方向上佩斯金问题的运动，并丢弃了切向弹性拉伸的贡献。该模型采用了完全非线性标量轮廓方程的形式。佩皮问题是一个流体结构的相互作用问题，它描述了浸入不可压缩的Stokes流体中的弹性杆的运动。我们证明了在关键Lipschitz空间中的初始数据的时代存在解决方案。使用新的分解以及取消属性，点式方法使我们能够在Lipschitz类中获得所需的估计值。此外，我们执行能量估计，以便获得解决方案位于$ l^2 \ left（[0，t]; h^{3/2} \ right）$中以满足轮廓方程的位置。
In this paper we study a toy model of the Peskin problem that captures the motion of the full Peskin problem in the normal direction and discards the tangential elastic stretching contributions. This model takes the form of a fully nonlinear scalar contour equation. The Peskin problem is a fluid-structure interaction problem that describes the motion of an elastic rod immersed in an incompressible Stokes fluid. We prove global in time existence of solution for initial data in the critical Lipschitz space. Using a new decomposition together with cancellation properties, pointwise methods allow us to obtain the desired estimates in the Lipschitz class. Moreover, we perform energy estimates in order to obtain that the solution lies in the space $L^2 \left( [0,T];H^{3/2} \right) $ to satisfy the contour equation pointwise.
