  We investigate the timescales of evolution of stellar coronae in response to
surface differential rotation and diffusion. To quantify this we study both the
formation time and lifetime of a magnetic flux rope in a decaying bipolar
active region. We apply a magnetic flux transport model to prescribe the
evolution of the stellar photospheric field, and use this to drive the
evolution of the coronal magnetic field via a magnetofrictional technique.
Increasing the differential rotation (i.e. decreasing the equator-pole lap
time) decreases the flux rope formation time. We find that the formation time
is dependent upon the geometric mean of the lap time and the surface diffusion
timescale. In contrast, the lifetime of flux ropes are proportional to the lap
time. With this, flux ropes on stars with a differential rotation of more than
eight times the solar value have a lifetime of less than two days. As a
consequence, we propose that features such as solar-like quiescent prominences
may not be easily observable on such stars, as the lifetimes of the flux ropes
which host the cool plasma are very short. We conclude that such high
differential rotation stars may have very dynamical coronae.
