{"paper":{"title":"Instability of point defects in a two-dimensional nematic liquid crystal model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Arghir Zarnescu, Luc Nguyen, Radu Ignat, Valeriy Slastikov","submitted_at":"2015-03-12T10:57:45Z","abstract_excerpt":"We study a class of symmetric critical points in a variational $2D$ Landau - de Gennes model where the state of nematic liquid crystals is described by symmetric traceless $3\\times 3$ matrices. These critical points play the role of topological point defects carrying a degree $\\frac k 2$ for a nonzero integer $k$. We prove existence and study the qualitative behavior of these symmetric solutions. Our main result is the instability of critical points when $k\\neq \\pm 1, 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03670","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"}