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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.09778 |
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| _version_ | 1866908826147487744 |
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| author | Li, Shun Yu, Yong |
| author_facet | Li, Shun Yu, Yong |
| contents | We analyze the dynamical (in)stability of nematic liquid crystals in the presence of external magnetic fields and Rapini-Papoular surface potential. The P-HAN transition is investigated using a simplified 3D Ericksen-Leslie system. We find the thickness threshold of the P-HAN transition. If the thickness of the nematic layer exceeds this threshold, there is a global-in-time suitable weak solution converging exponentially to a nontrivial equilibrium state as time tends to infinity. If the thickness is no more than the threshold, the global-in-time suitable weak solution has a trivial long-time asymptotic limit. Our results rigorously justify the P-HAN transition discussed in the physics literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09778 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Phase Transition With Rapini-Papoular Surface Anchoring Li, Shun Yu, Yong Analysis of PDEs We analyze the dynamical (in)stability of nematic liquid crystals in the presence of external magnetic fields and Rapini-Papoular surface potential. The P-HAN transition is investigated using a simplified 3D Ericksen-Leslie system. We find the thickness threshold of the P-HAN transition. If the thickness of the nematic layer exceeds this threshold, there is a global-in-time suitable weak solution converging exponentially to a nontrivial equilibrium state as time tends to infinity. If the thickness is no more than the threshold, the global-in-time suitable weak solution has a trivial long-time asymptotic limit. Our results rigorously justify the P-HAN transition discussed in the physics literature. |
| title | Phase Transition With Rapini-Papoular Surface Anchoring |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.09778 |