  In the recent work~\cite{Wang:2021p2}, the author proposed the expanded
Maxwell's equations for moving charged media system, which seems subtle.
Considering a very short time, we can approximately define the inertial frame
of reference. If we assume all the physical quantities are defined in the same
reference frame by default, Maxwell's equations for the static media system and
moving media system are definitely the traditional Maxwell's equations, which
are covariant and consistent with the two fundamental postulates of special
relativity. We even prove the covariance of Maxwell's equations explicitly by
considering the Lorentz transformation under the ${\cal O} (v)$ order
approximation and the Galileo approximation, respectively. Therefore, it seems
to us that the fields in the expanded Maxwell's equations cannot be in the same
reference frame. Defining the fields in the lab and co-moving frames
explicitly, we derive the expanded Maxwell's equations for moving media system.
Furthermore, we discuss another possible variant of Maxwell's equations, which
has an additional coefficient $\alpha$ related to the media. However, it is
still subtle from theoretical point of view.
