Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590597 | Journal of Functional Analysis | 2012 | 30 Pages |
Abstract
We prove the following regularity result: any two-dimensional unit-length divergence-free vector field belonging to W1/p,p (p∈[1,2]) 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 (1⩽q<2), or by everywhere smooth unit-length vector fields (not necessarily divergence-free) and the approximation result holds in a weaker topology.
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