{"paper":{"title":"Unconditional uniqueness for the modified Korteweg-de Vries equation on the line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Didier Pilod, Luc Molinet, St\\'ephane Vento","submitted_at":"2014-11-20T21:53:27Z","abstract_excerpt":"We prove that the modified Korteweg- de Vries equation (mKdV) equation is unconditionally well-posed in $H^s(\\mathbb R)$ for $s> \\frac 13$. Our method of proof combines the improvement of the energy method introduced recently by the first and third authors with the construction of a modified energy. Our approach also yields \\textit{a priori} estimates for the solutions of mKdV in $H^s(\\mathbb R)$, for $s>0$, and enables us to construct weak solutions at this level of regularity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5707","kind":"arxiv","version":2},"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"}