  In this work, there are two parties, Alice on Earth and Bob on the satellite,
which initially share an entangled state, and some open problems, which emerge
during quantum steering that Alice remotely steers Bob, are investigated. Our
analytical results indicate that all entangled pure states and maximally
entangled evolution states (EESs) are steerable, and not every entangled
evolution state is steerable and some steerable states are only locally
correlated. Besides, quantum steering from Alice to Bob experiences a "sudden
death" with increasing decoherence strength. However, shortly after that,
quantum steering experiences a recovery with the increase of decoherence
strength in bit flip (BF) and phase flip (PF) channels. Interestingly, while
they initially share an entangled pure state, all EESs are steerable and obey
Bell nonlocality in PF and phase damping channels. In BF channels, all
steerable states can violate Bell-CHSH inequality, but some EESs are unable to
be employed to realize steering. However, when they initially share an
entangled mixed state, the outcome is different from that of the pure state.
Furthermore, the steerability of entangled mixed states is weaker than that of
entangled pure states. Thereby, decoherence can induce the degradation of
quantum steering, and the steerability of state is associated with the
interaction between quantum systems and reservoirs.
