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

Fanghua Lin, Changyou Wang

Research output: Contribution to journalArticle

Abstract

For any bounded smooth domain Ω ⊂ ℝ3 (or Ω = ℝ3), we establish the global existence of a weak solution (u, d) : Ω × [0, +∞) → ℝ3 × S2 of the initial boundary value (or the Cauchy) problem of the simplified Ericksen-Leslie system (1.1) modeling the hydrodynamic flow of nematic liquid crystals for any initial and boundary (or Cauchy) data (u0, d0) є H × H1(Ω, S2), with d0(Ω) ⊂ S2 (the upper hemisphere). Furthermore, (u, d) satisfies the global energy inequality (1.4).

Original languageEnglish (US)
Pages (from-to)1532-1571
Number of pages40
JournalCommunications on Pure and Applied Mathematics
Volume69
Issue number8
DOIs
StatePublished - Aug 1 2016

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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