Two-dimensional unit-length vector fields of vanishing divergence

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• 作者：Radu Ignat ^{Radu.Ignat@math.u-psud.fr}
• 关键词：Sobolev spaces ; Eikonal equation ; Regularity ; Approximation ; Vortices ; Kinetic formulation ; Entropy
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 期刊代码：75_00221236
• 类别：mt
• 出版时间：15 April, 2012
• 卷：262
• 期：8
• 页码：3465-3494
• 文件大小：304 K

摘要

We prove the following regularity result: any two-dimensional unit-length divergence-free vector field belonging to () is locally Lipschitz except at a locally finite number of vortex-point singularities. We also prove approximation results for such vector fields: the dense sets are formed either by unit-length divergence-free vector fields that are smooth except at a finite number of points and the approximation result holds in the -topology (), or by everywhere smooth unit-length vector fields (not necessarily divergence-free) and the approximation result holds in a weaker topology.