Blow Up Criteria For The Incompressible Nematic Liquid Crystal Flows

In this paper, we investigate blow up criteria for the local smooth solutions to the 3D incompressible nematic liquid crystal flows via the components of the gradient velocity field (?)u and the gradient orientation field (?)d. More precisely, we show that 0< T*<+∞ is the maximal time if and only ifIt is consists of three chapters, its main content is as follows:In Chapter 1,briefly reviews the background and research status of the problem, introduces the characteristics of the incompressible liquid crystal flows and the main work of this paper.In Chapter 2, research blow up criteria for the local smooth solutions to the 3D incompressible nematic liquid crystal flows via the components of the gradient velocity field (?)u and the gradient orientation (?)d.In Chapter 3, research blow up criteria for the local smooth solutions to the 3D incompressible nematic liquid crystal flows via the components of the gradient velocity field (?)3u3 and the gradient orientation (?)d.