A regularity criterion for the 3D density-dependent incompressible flow of liquid crystals with vacuum
Volume 115 / 2015
Annales Polonici Mathematici 115 (2015), 165-177
MSC: Primary 35B65; Secondary 35Q35, 82D30.
DOI: 10.4064/ap115-2-4
Abstract
We consider the Cauchy problem for the $3$D 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 Fan–Li [Comm. Math. Sci. 12 (2014), 1185–1197].
