Vector Differential Equation

1. Dec 21, 2003

MathNerd

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.

Last edited by a moderator: Dec 21, 2003
2. Dec 21, 2003

Hurkyl

Staff Emeritus
If I recall correctly, the general solution is

$$\vec{V} = \nabla \times \vec{A} = \mathrm{curl} \vec{A}$$

for any (differentiable) vector field $\vec{A}$.