{"paper":{"title":"Global solutions and stability properties of the 5th order Gardner equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chulkwang Kwak, Miguel A. Alejo","submitted_at":"2019-01-10T19:19:45Z","abstract_excerpt":"In this work, we deal with the initial value problem of the 5th-order Gardner equation in $\\mathbb{R}$, presenting the local well-posedness result in $H^2(\\mathbb{R})$. As a consequence of the local result, in addition to $H^2$-energy conservation law, we are able to prove the global well-posedness result in $H^2(\\mathbb{R})$. Finally, we present a stability result for 5th order Gardner breather solution in the Sobolev space $H^2(\\mathbb{R})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03350","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"}