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June  2003, 2(2): 251-257. doi: 10.3934/cpaa.2003.2.251

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, United States

Received  October 2002 Revised  March 2003 Published  March 2003

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: existence, Curl, uniqueness., distribution.
Mathematics Subject Classification: 15A72, 35A10, 35D1.
Citation: Biao Ou. Examinations on a three-dimensional differentiable vector field that equals its own curl. Communications on Pure and Applied Analysis, 2003, 2 (2) : 251-257. doi: 10.3934/cpaa.2003.2.251
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