A diffuse-interface Landau-de Gennes model for free-boundary value problems in the theory of nematic liquid crystals

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Wu, Dawei and Shi, Baoming and Han, Yucen and Zhang, Pingwen and Majumdar, Apala and Zhang, Lei (2025) A diffuse-interface Landau-de Gennes model for free-boundary value problems in the theory of nematic liquid crystals. SIAM Journal on Mathematical Analysis, 57 (4). 4358 - 4395. ISSN 0036-1410 (https://doi.org/10.1137/24M1710322)

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Abstract

We introduce a diffuse-interface Landau-de Gennes free energy for nematic liquid crystals (NLC) systems, with free boundaries, in three dimensions submerged in isotropic liquid, and a phase field is introduced to model the deformable interface. The energy consists of the original Landau-de Gennes free energy, three penalty terms and a volume constraint. We prove the existence and regularity of minimizers for the diffuse-interface energy functional. We also prove a uniform maximum principle of the minimizer under appropriate assumptions, together with a uniqueness result for small domains. Then, we establish a sharp-interface limit where minimizers of the diffuse-interface energy converge to a minimizer of a sharp-interface energy using methods from Γ-convergence. Finally, we conduct numerical experiments with the diffuse-interface model and the findings are compared with existing works.

ORCID iDs

Wu, Dawei, Shi, Baoming, Han, Yucen, Zhang, Pingwen, Majumdar, Apala ORCID logoORCID: https://orcid.org/0000-0003-4802-6720 and Zhang, Lei;
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