The simplified 2D Ericksen-Leslie liquid crystal model interacting with a 1D flexible shell
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909022528995328 |
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| author | Mensah, Prince Romeo |
| author_facet | Mensah, Prince Romeo |
| contents | We consider the evolution and interaction of a 2-dimensional nematic liquid crystal of Ericksen-Leslie type within a 1-dimensional flexible viscoelastic structure. This is a fully macroscopic model in which the nematic liquid crystal is modelled by the simplified Ericksen-Leslie system with Ginzburg-Landau approximation. The liquid crystal is contained in a thin viscoelastic shell of arbitrary reference configuration that evolves with respect to the forces exerted by the liquid crystal. Barring any degeneracies in the shell, we construct a global weak solution for the coupled system. We then show that any family of such weak solutions that are parametrized by the Ginzburg-Landau coefficient, converges to a weak solution of the original simplified Ericksen-Leslie system without the Ginzburg-Landau term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06463 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The simplified 2D Ericksen-Leslie liquid crystal model interacting with a 1D flexible shell Mensah, Prince Romeo Analysis of PDEs We consider the evolution and interaction of a 2-dimensional nematic liquid crystal of Ericksen-Leslie type within a 1-dimensional flexible viscoelastic structure. This is a fully macroscopic model in which the nematic liquid crystal is modelled by the simplified Ericksen-Leslie system with Ginzburg-Landau approximation. The liquid crystal is contained in a thin viscoelastic shell of arbitrary reference configuration that evolves with respect to the forces exerted by the liquid crystal. Barring any degeneracies in the shell, we construct a global weak solution for the coupled system. We then show that any family of such weak solutions that are parametrized by the Ginzburg-Landau coefficient, converges to a weak solution of the original simplified Ericksen-Leslie system without the Ginzburg-Landau term. |
| title | The simplified 2D Ericksen-Leslie liquid crystal model interacting with a 1D flexible shell |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.06463 |