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Math Help - Divergence reverse process

  1. #1
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    Divergence reverse process

    can anyone plz tell me how to get F(vector field) when im given DIV F(div means divergence )
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  2. #2
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    What makes you think it's possible?

    F=(-y,xy,z), divF=x+1
    G=(x^2/2,y,-xy), divG=x+1
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  3. #3
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    well i think there will be some way ....
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  4. #4
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    Well, you can always say: Let S be the set of all possible vector fields F such that div F=x+1. In that case, the two examples I just gave you would both be elements in S. But you seem to be asking your question with the assumption that there is a one-to-one correspondence between vector fields and their divergences. This is not the case.
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  5. #5
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    To add further, since \nabla \cdot \nabla \times {\bf F} = 0 where  {\bf F} is an arbitrary vector field, then you can add \nabla \times {\bf F} to your vector field and it will lead to the same diverence.
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