Maxwell equations and special relativety

They are Lorentz invariant, infact you need the Lorentz transformation in order to make sure that they do not vary between inertial frames (which would be very troublesome).

 

Indeed, they are, in sense, the whole point of relativity. Maxwell's equations did not agree with "Galillean" relativity which seemed to imply that all speeds had to be measured relative to some absolute fixed point. Repeated experiments showed that that was not true. Relativity extended Galillean relativity to include electro-magnetic effects.

 

And also: A certain solution to the Maxwell equations is a description of a wave moving at a speed [itex]1/ \sqrt{\epsilon_0 \mu_0} [/itex] wich can be calculated to be about 300.000 km/s =c or the speed of light. Together with the Lorentz transformation rules wich the Maxwell equations obey this implies that light is an electromagnetic phenomena and propagates at a fixed speed. This is one of the axioms of SR.