Phase Transition With Rapini-Papoular Surface Anchoring
Analysis of PDEs
2026-02-11 v1
Abstract
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.
Cite
@article{arxiv.2602.09778,
title = {Phase Transition With Rapini-Papoular Surface Anchoring},
author = {Shun Li and Yong Yu},
journal= {arXiv preprint arXiv:2602.09778},
year = {2026}
}
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64 pages