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A regularity criterion for the 3D density-dependent incompressible flow of liquid crystals with vacuum. (English) Zbl 1339.35253

Summary: We consider the Cauchy problem for the 3D density-dependent incompressible flow of liquid crystals with vacuum, and provide a regularity criterion in terms of \(\boldsymbol u\) and \(\nabla {\boldsymbol d}\) in the Besov spaces of negative order. This improves a recent result of J. Fan and F. Li [Commun. Math. Sci. 12, No. 7, 1185-1197 (2014)].

MSC:

35Q35 PDEs in connection with fluid mechanics
35B65 Smoothness and regularity of solutions to PDEs
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
76A15 Liquid crystals
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