BLOW-UP CRITERION OF CLASSICAL SOLUTIONS FOR THE INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

摘要

In this paper,we consider the short time classical solution to a simplified hydrodynamic flow modeling incompressible,nematic liquid crystal materials in R^3. We establish a criterion for possible breakdown of such solutions at a finite time. More precisely,if(u,d)is smooth up to time T provided that ∫_0~T||▽×u(t,·)||_(BMO)(R^3)+||▽d(t,·)||_(L^4(R^3))~8dt<∞.