Consider the differential equation curl f = f for a 3-dimensional differentiable vector field f. We prove that f is analytic and then prove an existence and uniqueness theorem for the differential equation with a prescribed boundary data. We also outline with a few variations Professor J. Ericksen's work on a unit vector field that equals its own curl.
Institute for Mathematics and Its Applications>IMA Preprints Series
Examinations on a Three-Dimensional Differentiable Vector Field That Equals its Own Curl.
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