On the motion of the director field of a nematic liquid crystal submitted to a magnetic field and a laser beam

Paulo Amorim; João Paulo Dias; Assis F. Martins

doi:10.1007/s42985-023-00256-w

On the motion of the director field of a nematic liquid crystal submitted to a magnetic field and a laser beam

Paulo Amorim, João Paulo Dias, Assis F. Martins

DCM - Departamento de Ciência dos Materiais

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

1 Citation (Scopus)

Abstract

We study the motion of the director field of a nematic liquid crystal submitted to a magnetic field and to a laser beam. The problem takes the form of a quasilinear wave equation in a single space variable, coupled to a Schrödinger equation. We prove the existence of a global weak solution for the initial value problem using a viscous approximation and the compensated compactness method. We finish with some numerical computations to illustrate the results.

Original language	English
Article number	36
Number of pages	14
Journal	Partial Differential Equations and Applications
Volume	4
Issue number	4
DOIs	https://doi.org/10.1007/s42985-023-00256-w
Publication status	Published - Aug 2023

Keywords

Cauchy problem
Laser beam
Liquid crystal
Magnetic field
Nematic

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10.1007/s42985-023-00256-w

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title = "On the motion of the director field of a nematic liquid crystal submitted to a magnetic field and a laser beam",

abstract = "We study the motion of the director field of a nematic liquid crystal submitted to a magnetic field and to a laser beam. The problem takes the form of a quasilinear wave equation in a single space variable, coupled to a Schr{\"o}dinger equation. We prove the existence of a global weak solution for the initial value problem using a viscous approximation and the compensated compactness method. We finish with some numerical computations to illustrate the results.",

keywords = "Cauchy problem, Laser beam, Liquid crystal, Magnetic field, Nematic",

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doi = "10.1007/s42985-023-00256-w",

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T1 - On the motion of the director field of a nematic liquid crystal submitted to a magnetic field and a laser beam

AU - Amorim, Paulo

AU - Dias, João Paulo

AU - Martins, Assis F.

N1 - info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04561%2F2020/PT# Funding Information: P. Amorim was partially supported by Conselho Nacional de Pesquisa (CNPq) grant No. 308101/2019-7. Publisher Copyright: © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2023/8

Y1 - 2023/8

N2 - We study the motion of the director field of a nematic liquid crystal submitted to a magnetic field and to a laser beam. The problem takes the form of a quasilinear wave equation in a single space variable, coupled to a Schrödinger equation. We prove the existence of a global weak solution for the initial value problem using a viscous approximation and the compensated compactness method. We finish with some numerical computations to illustrate the results.

AB - We study the motion of the director field of a nematic liquid crystal submitted to a magnetic field and to a laser beam. The problem takes the form of a quasilinear wave equation in a single space variable, coupled to a Schrödinger equation. We prove the existence of a global weak solution for the initial value problem using a viscous approximation and the compensated compactness method. We finish with some numerical computations to illustrate the results.

KW - Cauchy problem

KW - Laser beam

KW - Liquid crystal

KW - Magnetic field

KW - Nematic

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DO - 10.1007/s42985-023-00256-w

M3 - Article

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SN - 2662-2963

VL - 4

JO - Partial Differential Equations and Applications

JF - Partial Differential Equations and Applications

IS - 4

M1 - 36

ER -

On the motion of the director field of a nematic liquid crystal submitted to a magnetic field and a laser beam

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