Blow-up criterion of classical solutions for the incompressible nematic liquid crystal flows

Abstract

In this paper, we consider the short time classical solution to a simplified hydrodynamic flow modeling incompressible, nematic liquid crystal materials in dimension three. 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 ${\int }_0^T|\nabla \times u(t,\cdot ){|}_{BMO({\mathbb{R}}^3)}+|\nabla d(t,\cdot ){|}_{L^4({\mathbb{R}}^3)}^{8}dt<\infty$

arXiv commentThis paper has been withdrawn by the author due to a crucial sign error in equation 1 You may also update the abstract