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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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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.

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Acknowledgements

J. P. Dias is indebted to H. Frid, V. Konotop, and E. Ducla Soares for interesting remarks and was partially supported by the Fundação para a Ciência e Tecnologia (FCT) through grant UIDB/04561/2020. P. Amorim was partially supported by Conselho Nacional de Pesquisa (CNPq) grant No. 308101/2019-7.

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Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, Rio de Janeiro, RJ, C.P. 68530, 21941-909, Brasil

    Paulo Amorim

  2. CMAFcCIO and Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, Edifício C6, 1749-016, Lisbon, Portugal

    João-Paulo Dias

  3. Departamento de Ciência dos Materiais, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    Assis F. Martins

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  1. Paulo Amorim
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  2. João-Paulo Dias
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Correspondence to Paulo Amorim.

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This article is part of the section “Theory of PDEs” edited by Eduardo Teixeira.

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Amorim, P., Dias, JP. & Martins, A.F. On the motion of the director field of a nematic liquid crystal submitted to a magnetic field and a laser beam. Partial Differ. Equ. Appl. 4, 36 (2023). https://doi.org/10.1007/s42985-023-00256-w

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  • DOI: https://doi.org/10.1007/s42985-023-00256-w

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