Examinations on a three-dimensional differentiable vector field that equals its own curl

Biao Ou

doi:10.3934/cpaa.2003.2.251

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2003, Volume 2, Issue 2: 251-257. Doi: 10.3934/cpaa.2003.2.251

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Examinations on a three-dimensional differentiable vector field that equals its own curl

Biao Ou^1,

1.
Department of Mathematics, University of Toledo, Toledo OH 43606

Received: October 2002

Revised: March 2003

Published: June 2003

Abstract Related Papers Cited by

Abstract

Consider a three-dimensional differentiable vector field $f$ that equals its own curl. We prove that $f$ is analytic and then establish an existence and uniqueness theorem for such a vector field satisfying a prescribed boundary condition. We also outline with a few variations Professor J. Ericksen's work on a unit vector field that equals its own curl.

Keywords:

Curl,
distribution,
existence,
uniqueness.

Mathematics Subject Classification: 15A72, 35A10, 35D10.

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