We study the curves of coherence for the Bell-diagonal states including l_1-norm of coherence and relative entropy of coherence under the Markovian channels in the first subsystem once. For a special Bell-diagonal state under bit-phase flip channel, we find frozen coherence under l_1 norm occurs, but relative entropy of coherence decrease. It illustrates that the occurrence of frozen coherence depends on the type of the measure of coherence. We study the coherence evolution of Bell-diagonal

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... es under Markovian channels in the first subsystem n times and find coherence under depolarizing channel decreases initially then increases for small n and tend to zero for large n. We discuss the dynamics of coherence of the Bell-diagonal state under two independent same type local Markovian channels. We depict the dynamic behaviors of relative entropy of coherence for Bell-diagonal state under the bi-side different Markovian channel. We depict the dynamic behaviors of relative entropy of coherence for Bell-diagonal state under the bi-side different Markovian channel.