LPS's Criterion for Incompressible Nematic Liquid Crystal Flows

Abstract

In this paper we derive LPS's criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in ${\mathbb{R}}^3$. We show that if $0<T<+\infty$} is the maximal time interval for the unique smooth solution $u\in C^{\infty }([0,T),{\mathbb{R}}^3)$, then $|u|+|\nabla d|\notin L^q([0,T],L^p({\mathbb{R}}^3))$, where $p$ and $q$ safisfy the Ladyzhenskaya-Prodi-Serrin's condition: $\frac{3}{p}+\frac{2}{q}=1$ and $p\in (3,+\infty ]$

arXiv admin note: substantial text overlap with arXiv:1210.4140

References in corpus (1)

• Logarithmical Blow-up Criteria for the Nematic Liquid Crystal Flows