{"paper":{"title":"Some results on the penalised nematic liquid crystals driven by multiplicative noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erika Hausenblas, Paul Razafimandimby, Zdzislaw Brze\\'zniak","submitted_at":"2013-10-31T19:03:26Z","abstract_excerpt":"In this paper we prove several results related to the existence and uniqueness of solution to coupled highly nonlinear stochastic partial differential equations (PDEs). These equations are motivated by the dynamics of nematic liquid crystals under the influence of stochastic external forces. Firstly, we prove the existence of global weak solution (in sense of both stochastic analysis and PDEs). We show the pathwise uniqueness of the solution in 2D domain. Secondly, we establish the existence and uniqueness of local maximal solution which is strong in sense of both PDEs and stochastic analysis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8641","kind":"arxiv","version":3},"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"}