{"paper":{"title":"Remarks on the Gibbs measures for nonlinear dispersive equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Laurent Thomann (LMJL), Nicolas Burq (LM-Orsay), Nikolay Tzvetkov (AGM)","submitted_at":"2014-12-23T20:14:38Z","abstract_excerpt":"We show, by the means of several  examples,  how we can use Gibbs measures to construct global solutions to dispersive equations at low regularity.  The construction relies on  the Prokhorov compactness theorem combined with the Skorokhod convergence theorem. To begin with, we  consider  the non linear Schr\\\"odinger equation (NLS) on the tri-dimensional sphere. Then we focus on  the Benjamin-Ono equation and on  the derivative nonlinear Schr\\\"odinger equation on the circle. Next, we construct a Gibbs measure and global solutions to the so-called periodic half-wave equation. Finally, we conside"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7499","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"}