Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook