Examinations on a Three-Dimensional Differentiable Vector Field That Equals its Own Curl

Ou, Biao2007-08-162007-08-162001-07https://hdl.handle.net/11299/3683Consider 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.Examinations on a Three-Dimensional Differentiable Vector Field That Equals its Own Curl