论文标题
在双限度流的自相似奇点形成上
On self-similar singularity formation for the binormal flow
论文作者
论文摘要
本文的目的是为在某些限制性情况下比[5]建立一个简洁的证据，以实现双重流动的自相似解决方案的稳定性结果。该方程式也称为局部诱导近似值，是涡旋细丝动力学的标准模型，其自相似解描述了细丝上角奇异性的形成。我们的方法强烈使用了Hasimoto在1972年在二手流的解和1-DCupicSchrödinger方程之一之间指出的联系，以及与后者相关的存在结果。
The aim of this article is to establish a concise proof for a stability result of self-similar solutions of the binormal flow, in some more restrictive cases than in [5]. This equation, also known as the Local Induction Approximation, is a standard model for vortex filament dynamics, and its self-similar solution describes the formation of a corner singularity on the filament. Our approach strongly uses the link that Hasimoto pointed out in 1972 between the solution of the binormal flow and the one of the 1-D cubic Schrödinger equation, as well as the existence results associated to the latter.
