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Communications on Pure and Applied Analysis (CPAA)
 

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

Pages: 251 - 257, Volume 2, Issue 2, June 2003      doi:10.3934/cpaa.2003.2.251

 
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Biao Ou - Department of Mathematics, University of Toledo, Toledo OH 43606, United States (email)

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.

Received: October 2002;      Revised: March 2003;      Available Online: March 2003.