Global Well-posedness for the Density-Dependent Incompressible Flow of Liquid Crystals

Abstract

In the present paper, we consider the global well-posedness of the density-dependent incompressible flow of liquid crystals in $\mathbb{R}^{2}$ . The local existence and uniqueness of the system are obtained without the assumption of small density variation. The global well-posedness is proved when the initial density and liquid crystal orientation are small. However, the initial velocity field is allowed to be arbitrarily large.