Abstract
We provide a sufficient condition for the regularity of solutions to the 3D nematic liquid crystal flow in the Morrey–Campanato space. More precisely, we prove that if the velocity u satisfies ∫0T‖u(⋅,t)‖Ṁp,3r21−r1+ln(e+‖u(⋅,t)‖L6)dt<∞with 0<r<1 and 2≤p≤3r, or the gradient of the velocity ∇u satisfies ∫0T‖∇u(⋅,t)‖Ṁp,3γ22−γ1+ln(e+‖u(⋅,t)‖L6)dt<∞with 0<γ≤1 and 2≤p≤3γ, then the solution (u,d) remains smooth on (0,T].
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