标题： 粘性涡旋丝的演化和Biot-Savart积分的去奇异化 显示英文标题

标题： Evolution of viscous vortex filaments and desingularization of the Biot-Savart integral

摘要： 我们考虑一种运动粘度为$\nu $的粘性流体，初始数据由一个光滑的闭合涡旋丝线组成，其环量为$\Gamma $。 我们证明，在足够短的时间内，解由一个变形的 Lamb-Oseen 涡旋组成，其中心（一条丝线）遵循法线方向流动的动力学，并加上依赖于丝线曲率和丝线远距离部分非局部相互作用的高阶修正项。 为了实现这种尺度分离，我们需要$\Gamma /\nu $足够小。 显示英文摘要

摘要： We consider a viscous fluid with kinematic viscosity $\nu $ and initial data consisting of a smooth closed vortex filament with circulation $\Gamma $. We show that, for short enough time, the solution consists of a deformed Lamb-Oseen vortex whose center (a filament) follows the binormal flow dynamics plus leading order corrections that depend locally on the filament curvature and the nonlocal interactions with distant parts of the filament. In order to achieve this scale separation we require $\Gamma /\nu $ to be sufficiently small.