Divergence and rotational equal to zero - solutions?

Tosh5457 · Dec 11, 2011

Hi, I'd like to know the solutions for these equations, and how to arrive at them. Is it possible to derive the general form of F(x,y,z) analytically? I'm still studying linear differential equations so I have no clue on what to do with partial differential equations...

div F = 0
curl F = 0

Thanks :)

dextercioby · Dec 12, 2011

Doesn't this lead to Laplace equation ?

Tosh5457 · Dec 12, 2011

dextercioby said:

Doesn't this lead to Laplace equation ?

Yes, it leads to the vectorial Laplace equation (each component's laplacian is 0).

dextercioby · Dec 13, 2011

Vectorial ? No, scalar, take curl F=0. Then F = grad phi. Phi is a scalar. Phi will be involved in a scalar equation.

Divergence and rotational equal to zero - solutions?

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