{"paper":{"title":"On the regularity of the flow map for the gravity-capillary equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Spirn, J. Douglas Wright, Jeremy L. Marzuola, Robin Ming Chen","submitted_at":"2011-11-22T22:54:49Z","abstract_excerpt":"We prove via explicitly constructed initial data that solutions to the gravity-capillary wave system in $\\mathbb{R}^3$ representing a 2d air-water interface immediately fails to be $C^3$ with respect to the initial data if the initial data $(h_0, \\psi_0) \\in H^{s+\\frac12} \\otimes H^{s}$ for $s<3$. Similar results hold in $\\mathbb{R}^2$ domains with a 1d interface. Furthermore, we discuss the illposedness threshold for the pure gravity water wave system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5361","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"}