Abstract
In this paper, we provide a sufficient condition, in terms of the horizontal gradient of two horizontal velocity components and the gradient of liquid crystal molecular orientation field, for the breakdown of local in time strong solutions to the three‐dimensional incompressible nematic liquid crystal flows. More precisely, let T∗ be the maximal existence time of the local strong solution (u,d), then T∗<+∞ if and only if urn:x-wiley:mma:media:mma4014:mma4014-math-0001 where uh=(u1,u2), ∇h=(∂1,∂2). This result can be regarded as the generalization of the well‐known Beale‐Kato‐Majda (BKM) type criterion and is even new for the three‐dimensional incompressible Navier–Stokes equations. Copyright © 2016 John Wiley & Sons, Ltd.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
