具有黏度对比的 Peskin 问题
The Peskin Problem with Viscosity Contrast
AI总结：
针对内外黏度不同的 Peskin 问题，本文分析净力与自由界面的非局部耦合，证明临界空间中等尺寸初始界面的首个全局适定性及瞬时解析光滑化。
摘要：
Peskin 问题模拟浸没在不可压缩流体中的闭合弹性丝的动力学。本文考虑内、外黏度可能不同的情形。这种黏度对比通过净力与自由界面之间隐式的非局部关系，给系统增加了进一步的非局部效应。我们证明了该设定下 Peskin 问题的首个全局适定性结果。该结果适用于临界空间中的中等尺寸初始界面，并显示出瞬时解析光滑化。我们仔细计算了初始数据上的中等尺寸约束。即使没有黏度对比，这些结果也是新的。
英文摘要：
The Peskin problem models the dynamics of a closed elastic filament immersed in an incompressible fluid. In this paper, we consider the case when the inner and outer viscosities are possibly different. This viscosity contrast adds further non-local effects to the system through the implicit non-local relation between the net force and the free interface. We prove the first global well-posedness result for the Peskin problem in this setting. The result applies for medium size initial interfaces in critical spaces and shows instant analytic smoothing. We carefully calculate the medium size constraint on the initial data. These results are new even without viscosity contrast.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
