I was looking through a calculus book doing some of the practice problems where I was asked to calculate the curl of a few functions. One of them got me thinking, is there a function whose curl is itself? Much like how [itex]e^{x}[/itex] is it's own derivative, is there a vector field that is it's own curl?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]∇×F = F[/tex]

Are there any non-zero general solutions to this problem? This will expand to a system of 3 linear PDE's with 3 unknowns. The problem is, I'm new to PDE's and don't know how to solve them. I am familiar with ODE's to some extent, and I understand that the goal is to simplify a PDE into an ODE. So my question... how would I go about solving this problem? Do you know any good online references that would teach me? Thank you for your time.

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# Curl F = F, solve for F (PDE)

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