  We study the dynamics of the quantum battery capacity for the Bell-diagonal
states under Markovian channels on the first subsystem. We show that the
capacity increases for special Bell-diagonal states under amplitude damping
channel. The sudden death of the capacity occurs under depolarizing channel. We
also investigate the capacity evolution of Bell-diagonal states under Markovian
channels on the first subsystem $n$ times. It is shown that the capacity under
depolarizing channel decreases initially, then increases for small $n$ and tend
to zero for large $n$. We find that under bit flip channel and amplitude
damping channel, the quantum battery capacity of special Bell-diagonal states
tends to a constant for large $n$, namely, the frozen capacity occurs. The
dynamics of the capacity of the Bell-diagonal states under two independent same
type local Markovian channels is also studied.
