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Given Curl V, can you find V?

  1. Apr 24, 2010 #1
    Say V is a vector field.
    Is there a way (or rather a reasonable algorithm) to find V, given Curl V?

  2. jcsd
  3. Apr 24, 2010 #2


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    If I told you curlV=0, can you give me a bunch of different functions that satisfy this requirement?
  4. Apr 24, 2010 #3
    Okay, let's impose V satisfies boundary conditions on a (hyper)surface or something. (Though I don't remember the conditions for uniqueness and regularity and so on of PDE solutions)

    I guess I asked the wrong question.
    Is there a way to find V within a transformation in what we might call the Kernel of the curl operator?

    (Like when someone asks what differentiates to f, it's understood that we can add a constant...)
  5. Apr 25, 2010 #4
    Yes, if the domain is good enough. The conventional way to phrase the problem is: given a vector field T with div T = 0, find V so that curl V = T. This should be in all multivariable calculus textbooks. But perhaps only after the discussion of vector integration.
  6. Apr 25, 2010 #5


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    You can determine V out of its curl, up to an arbitrary gradient field.
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