Observations of hard X-ray emission from the Vela pulsar wind nebula (PWN) with the ISGRI camera aboard INTEGRAL gamma-ray observatory have been analysed with the aim to search for possible flux variability on scales from weeks to years, which could be caused by short-term evolution of pulsar wind structures similar to those governing sharp flares and flux depressions observed in the sub-GeV emission of the Crab PWN. No statistically significant flux depressions or flares have been found in none of the considered energy ranges: 20-50 keV, 50-100 keV, and 100-200 keV, however some hints of flux instability can be seen in the former two bands. If the variability of the pulsar wind termination surface or instabilities of turbulent magnetic field in the nebula predicted by a number of PWN models indeed influence the synchrotron spectrum of such objects, the variability of the 1-30 MeV emission from the Vela PWN could be checked with the next generation of gamma-ray facilities, like eASTROGAM or HERMES.
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