On strong dynamics of compressible nematic liquid crystals

Katharina Schade; Yoshihiro Shibata

doi:10.1137/140970628

On strong dynamics of compressible nematic liquid crystals

Katharina Schade, Yoshihiro Shibata

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

Given a uniform W^3-1/q_q -domain ω ⊆ ℝ^N 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 language	English
Pages (from-to)	3963-3992
Number of pages	30
Journal	SIAM Journal on Mathematical Analysis
Volume	47
Issue number	5
DOIs	https://doi.org/10.1137/140970628
Publication status	Published - 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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10.1137/140970628

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AU - Schade, Katharina

AU - Shibata, Yoshihiro

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AB - 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.

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On strong dynamics of compressible nematic liquid crystals

Abstract

Keywords

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