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Vector Differential Equation

  1. Dec 21, 2003 #1
    V(x,y,z) is a cartesian vector field with components X(x,y,z), Y(x,y,z) and Z(x,y,z) respectively. I am just wondering what is the general form of the functions X, Y and Z as solutions to div( V ) = 0? Where div( V ) is the divergence of the vector field.

    Thanks in advance.
    Last edited by a moderator: Dec 21, 2003
  2. jcsd
  3. Dec 21, 2003 #2


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    If I recall correctly, the general solution is

    [tex]\vec{V} = \nabla \times \vec{A} = \mathrm{curl} \vec{A}[/tex]

    for any (differentiable) vector field [itex]\vec{A}[/itex].
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