具有Rapini-Papoular表面锚定的相变
Phase Transition With Rapini-Papoular Surface Anchoring
AI总结：
本文研究了在外部磁场和Rapini-Papoular表面势作用下向列液态晶体的P-HAN相变，通过简化三维Ericksen-Leslie系统确定了相变的厚度阈值，并证明了不同厚度条件下解的长期行为。
摘要：
我们分析了在存在外部磁场和Rapini-Papoular表面势的情况下，向列液态晶体的动力学（不）稳定性。利用简化后的三维Ericksen-Leslie系统研究了P-HAN转变。我们找到了P-HAN转变的厚度阈值。如果向列层的厚度超过该阈值，则存在全局时间内的合适弱解，该解随时间趋于无穷大而以指数形式收敛到一个非平凡的平衡态。如果厚度不超过阈值，则全局时间内的合适弱解具有平凡的长时间渐进行为。我们的结果严格证明了物理文献中讨论的P-HAN转变。
英文摘要：
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.
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