This question already has an answer here:
EM wave phenomenon is usually described as "changing electric field creates changing magnetic field which creates a changing electric field etc."
But fields of a uniformly moving (not accelerating) charge also change, and as far as I can see, all the second-order derivatives in time and space required by the wave equation are in place (because of the 1/r^2 dependence).
So, why doesn't the field of a uniformly moving charge create EM waves all by itself, because of all the second-order derivatives? It seems to me that mathematics requires it.