Abstract
In Li–Liu–Zhong (Nonlinearity 30 (2017) 4062–4088), the authors proved the existence of a unique global strong solution to the Cauchy problem of 2D nonhomogeneous incompressible nematic liquid crystal flows with vacuum as far-field density provided the initial data density and the gradient of orientation decay not too slow at infinity, and the basic energy ‖ρ0u0‖L22+‖∇d0‖L22 is small. In this note, we aim at precisely describing this smallness condition.
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