{"paper":{"title":"On the well-posedness, ill-posedness and norm-inflation for a higher order water wave model on a periodic domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mahendra Panthee, Ricardo Pastran, Xavier Carvajal","submitted_at":"2019-08-20T17:42:43Z","abstract_excerpt":"In this work we are interested in the well-posedness issues for the initial value problem associated with a higher order water wave model posed on a pe\\-rio\\-dic domain $\\mathbb{T}$. We derive some multilinear estimates and use them in the contraction mapping argument to prove local well-posedness for initial data in the periodic Sobolev space $H^s(\\mathbb{T})$, $s\\geq 1$. With some restriction on the parameters appeared in the model, we use the conserved quantity to obtain global well-posedness for given data with Sobolev regularity $s\\geq 2$. Also, we use splitting argument to improve the gl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07508","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07508/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}