Global Existence of Weak Solutions of the Nematic Liquid Crystal Flow in Dimension Three

Abstract

Abstract For any bounded smooth domain , we establish the global existence of a weak solution of the initial boundary value (or the Cauchy) problem of the simplified Ericksen‐Leslie system LLF modeling the hydrodynamic flow of nematic liquid crystals for any initial and boundary (or Cauchy) data , with (the upper hemisphere). Furthermore, ( u , d ) satisfies the global energy inequality.© 2016 Wiley Periodicals, Inc.