Strong solutions of the compressible nematic liquid crystal flow

Abstract

We study strong solutions of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in a domain $\Omega \subset {\mathbb{R}}^3$. We first prove the local existence of unique strong solutions provided that the initial data ${\rho }_0,u_0,d_0$are sufficiently regular and satisfy a natural compatibility condition. The initial density function ${\rho }_0$ may vanish on an open subset (i.e., an initial vacuum may exist). We then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities $\Vert \rho {\Vert }_{L_t^{\infty }{L}_x^{\infty }}$ and $\Vert \nabla d{\Vert }_{L_t^3{L}_x^{\infty }}$.

References in corpus (2)

• A blow-up criterion for the compressible liquid crystals system
• Serrin Type Criterion for the Three-Dimensional Viscous Compressible Flows

Cited by in corpus (2)

• Blow up criterion for compressible nematic liquid crystal flows in dimension three
• On Multi-dimensional Compressible Flows of Nematic Liquid Crystals with Large Initial Energy in a Bounded Domain