{"paper":{"title":"The well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesco Fanelli, Rapha\\\"el Danchin","submitted_at":"2013-05-06T09:48:58Z","abstract_excerpt":"This work is the continuation of the recent paper \\cite{D2} devoted to the density-dependent incompressible Euler equations. Here we concentrate on the well-posedness issue in Besov spaces of type $B^s_{\\infty,r}$ embedded in the set of Lipschitz continuous functions, a functional framework which contains the particular case of H\\\"older spaces and of the endpoint Besov space $B^1_{\\infty,1}.$ For such data and under the nonvacuum assumption, we establish the local well-posedness and a continuation criterion in the spirit of that of Beale, Kato and Majda in \\cite{BKM}.\n  In the last part of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1129","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"}