In this work, we study the regularity criterion of the three-dimensional nematic liquid crystal flows. It is proved that if the vorticity satisfies ∫0 T∥ω(t,ṡ)∥ B.∞,∞-12/1+log(e+∥ω(t,ṡ) ∥B.∞,∞ -1)dt<∞, where B.∞,∞-1 denotes the critical Besov space, then the solution (u,d) becomes a regular solution on (0,T]. This result extends the recent regularity criterion obtained by Fan and Ozawa (2012).

Logarithmically improved regularity criterion for the nematic liquid crystal flows in $dot{B}^{-1}_{infty,infty}$

RAGUSA, Maria Alessandra
2013-01-01

Abstract

In this work, we study the regularity criterion of the three-dimensional nematic liquid crystal flows. It is proved that if the vorticity satisfies ∫0 T∥ω(t,ṡ)∥ B.∞,∞-12/1+log(e+∥ω(t,ṡ) ∥B.∞,∞ -1)dt<∞, where B.∞,∞-1 denotes the critical Besov space, then the solution (u,d) becomes a regular solution on (0,T]. This result extends the recent regularity criterion obtained by Fan and Ozawa (2012).
2013
Regularity; Nematic liquid crystal; Navier-Stokes equation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/14094
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