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 u and ∇d in the Besov spaces of negative order. This improves a recent result of Fan-Li [Comm. Math. Sci. 12 (2014), 1185-1197].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-2-4, author = {Zujin Zhang and Xian Yang}, title = {A regularity criterion for the 3D density-dependent incompressible flow of liquid crystals with vacuum}, journal = {Annales Polonici Mathematici}, volume = {113}, year = {2015}, pages = {165-177}, zbl = {06487231}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-2-4} }
Zujin Zhang; Xian Yang. A regularity criterion for the 3D density-dependent incompressible flow of liquid crystals with vacuum. Annales Polonici Mathematici, Tome 113 (2015) pp. 165-177. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-2-4/