The so-called "electromagnetic wave equation" is so general that it should obviously hold for every point in space and for all field configurations (if there are no charges).
Here it is: $$ \left(c^2 \nabla^2 - \dfrac{\partial^2}{\partial t^2}\right)\mathbf E = 0$$
Now, for a uniformly moving (not accelerating) charge, the field configuration "moves" with it, with velocity $v$ (let's ignore relativistic effects).
Although this is no "wave", any function that "moves" should satisfy its own "wave equation", but with $v^2$ instead of $c^2$.
(is that right?)
But now we have a contradiction, because in my example the electic field is supposed to satisfy two different equations at once.
Where is the mistake? I'll appreciate any input.
