We establish the regularity of weak solutions for the vorticity equation associated to a family of desingularized models for vortex filament dynamics in 3D incompressible viscous flows. These generalize the classical model ‘of an allowance for the thickness of the vortices’ due to Louis Rosenhead in 1930. Our approach is based on an interplay between the geometry of vorticity and analytic inequalities in Sobolev spaces.

中文翻译：

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不可压缩粘性流中涡旋丝的异化模型的规则性：一种几何方法

我们为与3D不可压缩粘性流中的涡旋丝动力学动力学的去奇化模型族相关的涡度方程建立弱解的规律。这些归纳了路易斯·罗森黑德在1930年提出的经典模型“允许涡旋厚度的余量”。我们的方法是基于Sobolev空间中涡旋几何和解析不等式之间的相互作用。