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Glitches correspond to sudden jumps of rotation frequency ($\nu$) and itsderivative ($\dot{\nu}$) of pulsars, the origin of which remains not wellunderstood yet, partly because the jump processes of most glitches are not welltime-resolved. There are three large glitches of the Crab pulsar, detected in1989, 1996 and 2017, which were found to have delayed spin-up processes beforethe normal recovery processes. Here we report two additional glitches of theCrab pulsar occurred in 2004 and 2011 for which we discovered delayed spin upprocesses, and present refined parameters of the largest glitch occurred in2017. The initial rising time of the glitch is determined as $<0.48$ hour. Wealso carried out a statistical study of these five glitches with observedspin-up processes. The two glitches occurred in 2004 and 2011 have delayedspin-up time scales ($\tau_{1}$) of $1.7\pm0.8$\,days and $1.6\pm0.4$\,days,respectively. We find that the $\Delta{\nu}$ vs. $|\Delta{\dot\nu}|$ relationof these five glitches is similar to those with no detected delayed spin-upprocess, indicating that they are similar to the others in nature except thatthey have larger amplitudes. For these five glitches, the amplitudes of thedelayed spin-up process ($|\Delta{\nu}_{\rm d1}|$) and recovery process($\Delta{\nu}_{\rm d2}$), their time scales ($\tau_{1}$, $\tau_{2}$), andpermanent changes in spin frequency ($\Delta{\nu}_{\rm p}$) and total frequencystep ($\Delta{\nu}_{\rm g}$) have positive correlations. From thesecorrelations, we suggest that the delayed spin-up processes are common for allglitches, but are too short and thus difficult to be detected for mostglitches.

Discovery of delayed spin-up behavior following two large glitches in the Crab pulsar, and the statistics of such processes