{"paper":{"title":"Twisted solutions to a simplified Ericksen-Leslie equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Soojung Kim, Yong Yu, Yuan Chen","submitted_at":"2016-10-05T01:53:43Z","abstract_excerpt":"In this article we construct global solutions to a simplified Ericksen-Leslie system on $\\mathbb{R}^3$. The constructed solutions are twisted and periodic along the $x_3$-axis with period $d = 2\\pi \\big/ \\mu$. Here $\\mu > 0$ is the twist rate. $d$ is the distance between two planes which are parallel to the $x_1x_2$-plane. Liquid crystal material is placed in the region enclosed by these two planes. Given a well-prepared initial data, our solutions exist classically for all $t \\in [0, \\infty)$. However these solutions become singular at all points on the $x_3$-axis and escape into third dimens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01250","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}