{"paper":{"title":"Well-posedness and Continuity Properties of the Fornberg-Whitham Equation in Besov Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"John Holmes, Ryan C. Thompson","submitted_at":"2016-05-31T20:00:03Z","abstract_excerpt":"In this paper, we prove well-posedness of the Fornberg-Whitham equation in Besov spaces $B_{2,r}^s$ in both the periodic and non-periodic cases. This will imply the existence and uniqueness of solutions in the aforementioned spaces along with the continuity of the data-to-solution map provided that the initial data belongs to $B_{2,r}^s $. We also establish sharpness of continuity on the data-to-solution map by showing that it is not uniformly continuous from any bounded subset of $B_{2,r}^s$ to $C([-T,T]; B^s_{2,r})$. Furthermore, we prove a Cauchy-Kowalevski type theorem for this equation th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00010","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"}