My major achievement in the theoretical research on inductionless forms of magnetorotational instability is the disprovement of the so-called Liu limit for the helical magnetorotational instability (HMRI) and discovery of the existence of HMRI in the flows of matter rotating according to the Keplerian laws of celestial mechanics [1,2]. This result has opened prospects for modelling astrophysical phenomena happening in accretion disks in compact laboratory experiments with liquid metals. This work published in Phys. Rev. Lett. has attracted significant attention of world media in 2013.
 O.N. Kirillov, F. Stefani (2013) Extending the range of the inductionless magnetorotational instability. Physical Review Letters, 111(6): 061103
 O.N. Kirillov, F. Stefani, Y. Fukumoto (2014) Local instabilities in magnetized rotational flows: A short-wavelength approach. Journal of Fluid Mechanics, 760: 591- 633