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A regularity criterion for liquid crystal flows in terms of the component of velocity and the horizontal derivative components of orientation field
AIMS Mathematics 2022, 7(3): 4168-4175
Published: 15 March 2021
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In this paper, we establish a regularity criterion for the 3D nematic liquid crystal flows. More precisely, we prove that the local smooth solution ( u , d ) is regular provided that velocity component u 3 , vorticity component ω 3 and the horizontal derivative components of the orientation field h d satisfy

0 T | | u 3 | | L p 2 p p 3 + | | ω 3 | | L q 2 q 2 q 3 + | | h d | | L a 2 a a 3 d t < , w i t h 3 < p , 3 2 < q , 3 < a .

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