论文标题
2-D中切向佩皮问题的全球解决方案
Global Solutions to the Tangential Peskin Problem in 2-D
论文作者
论文摘要
我们在2-D中介绍了切向Peskin问题，这是一个具有非本地漂移的标量漂移扩散方程。它是从2-D Peskin问题的特殊环境中得出的新欧拉（Eulerian）透视图，其中无限的长长和笔直的1-D弹性字符串在平面自身诱导的Stokes流动中切向变形。对于满足自然弱假设的能量类别中的初始基准，我们证明了其全球解决方案的存在。这被认为是基于拉格朗日配方的佩斯金问题的现有分析中的超临界问题。建立了构造解决方案的规律性和长期行为。解决方案的唯一性在其他假设下得到证明。
We introduce the tangential Peskin problem in 2-D, which is a scalar drift-diffusion equation with a nonlocal drift. It is derived with a new Eulerian perspective from a special setting of the 2-D Peskin problem where an infinitely long and straight 1-D elastic string deforms tangentially in the Stokes flow induced by itself in the plane. For initial datum in the energy class satisfying natural weak assumptions, we prove existence of its global solutions. This is considered as a super-critical problem in the existing analysis of the Peskin problem based on Lagrangian formulations. Regularity and long-time behavior of the constructed solution is established. Uniqueness of the solution is proved under additional assumptions.
