On Multi-dimensional Compressible Flows of Nematic Liquid Crystals with Large Initial Energy in a Bounded Domain

Abstract

We study the global existence of weak solutions to a multi-dimensional simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals with large initial energy in a bounded domain $\Omega \subset {\mathbb{R}}^N$, where N=2 or 3. By exploiting a maximum principle, Nirenberg's interpolation inequality and a smallness condition imposed on the $N$-th component of initial direction field $\mf{d}_0$ to overcome the difficulties induced by the supercritical nonlinearity $|\nabla \mathbf{d}{|}^2\mathbf{d}$ in the equations of angular momentum, and then adapting a modified three-dimensional approximation scheme and the weak convergence arguments for the compressible Navier-Stokes equations, we establish the global existence of weak solutions to the initial-boundary problem with large initial energy and without any smallness condition on the initial density and velocity.

arXiv admin note: substantial text overlap with arXiv:1210.3565

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Cited by in corpus (11)

• Recent developments of analysis for hydrodynamic flow of nematic liquid crystals
• Long-time Behavior of Solution for the Compressible Nematic Liquid Crystal Flows in ${\mathbb{R}}^3$
• Global finite energy weak solutions to the compressible nematic liquid crystal flow in dimension three
• Global well-posedness and large time behavior for compressible non-isothermal nematic liquid crystal flows with vacuum at infinity
• The Optimal Decay Rate of Strong Solution for the Compressible Nematic Liquid Crystal Equations with Large Initial Data
• On well-posedness of Ericksen-Leslie's parabolic-hyperbolic liquid crystal model in compressible flow
• Global existence and incompressible limit in critical spaces for compressible flow of liquid crystals
• Asymptotic Behavior of Solution to the Incompressible Nematic Liquid Crystal Flows in R^3
• Existence of global weak solutions to the compressible Ericksen-Leslie system in dimension one
• Strong solution for compressible liquid crystal system with random force
• Global large solutions and incompressible limit for the compressible flow of liquid crystals