  The SDO EUV observations have revealed interesting characteristics of warm
coronal emissions, which peak soon after the hot coronal X-ray emissions peak
during a flare and then sometimes peak for a second time hours after the X-ray
flare peak. This flare type, with two warm coronal emission peaks but only one
X-ray peak, has been named the EUV late phase. These flares have the distinct
properties of i) having a complex magnetic field structure with two initial
sets of coronal loops, with one upper set overlaying a lower set, ii) having an
eruptive flare initiated in the lower set and disturbing both loop sets, iii)
having the hot coronal emissions emitted only from the lower set, and iv)
having the first peak of the warm coronal emissions associated with the lower
set and its second peak emitted from the upper set much later. The disturbance
of the coronal loops by the eruption is at about the same time, but the
relaxation and cooling down of the heated coronal loops during the post-flare
reconnections have different time scales with the longer, upper loops being
significantly delayed from the lower loops. The difference in these cooling
time scales is related to the difference between the two peak times of the warm
coronal emission and is also apparent in the decay profile of the X-ray
emissions having two distinct decays, with the first decay slope being steeper
and the delayed decay slope being smaller during the time of the warm coronal
emission second peak. The frequency and relationship of the EUV late-phase
decay times between the Fe XVI two flare peaks and X-ray decay slopes are
examined using three years of SDO/EVE data, and the X-ray dual-decay character
is then exploited to estimate the frequency of EUV late-phase flares during the
past four solar cycles. This study indicates that the frequency of EUV
late-phase flares peaks before and after each solar cycle minimum.
