On multi-dimensional compressible flows of nematic liquid crystals with large initial energy in a bounded domain

被引：85

作者：

Jiang, Fei ^{[1
]}

Jiang, Song ^{[2
]}

Wang, Dehua ^{[3
]}

机构：

[1] Fuzhou Univ, Coll Math & Comp Sci, Fuzhou 350108, Peoples R China

[2] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

[3] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2013年 / 265卷 / 12期

基金：

美国国家科学基金会;

关键词：

Liquid crystals; Compressible flows; Weak solutions; Weak convergence arguments; HYDRODYNAMIC FLOW; WELL-POSEDNESS; WEAK SOLUTION;

D O I：

10.1016/j.jfa.2013.07.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 of 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 d(0) to overcome the difficulties induced by the supercritical nonlinearity vertical bar del d vertical bar(2)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. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：3369 / 3397

页数：29