# American Institute of Mathematical Sciences

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

 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.
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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