On strong dynamics of compressible nematic liquid crystals

Katharina Schade, Yoshihiro Shibata

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

Given a uniform W3-1/qq -domain ω ⊆ ℝN for N q ∞, we consider a simplified Ericksen.Leslie system modeling the flow of compressible nematic liquid crystals based on Lin and Liu [Comm. Pure Appl. Math., 48 (1995), pp. 501.537]. We show the unique existence of local-intime strong solutions. Furthermore, if ω is bounded and initial data are chosen suitably small, we obtain global-in-time strong solutions. Our approach is based on maximal regularity estimates of the compressible Navier.Stokes equation by Enomoto, von Below, and Shibata [Ann. Univ. Ferrara, 60 (2014), pp. 55.89] and maximal regularity estimates for the Neumann problem as a consequence of Weis-fs 2001 vector-valued Fourier multiplier theorem.

Original languageEnglish
Pages (from-to)3963-3992
Number of pages30
JournalSIAM Journal on Mathematical Analysis
Volume47
Issue number5
DOIs
Publication statusPublished - 2015

Keywords

  • Compressible viscous fluid
  • Global solutions
  • Nematic liquid crystals
  • Quasi-linear parabolic evolution equations
  • Regularity

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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