{"paper":{"title":"Global regularities of two-dimensional density patch for inhomogeneous incompressible viscous flow with general density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ping Zhang, Xiao Liao","submitted_at":"2016-04-27T03:48:37Z","abstract_excerpt":"Toward the open question proposed by P.-L. Lions in \\cite{Lions96} concerning the propagation of regularities of density patch for viscous inhomogeneous flow, we first establish the global in time well-posedness of two-dimensional inhomogeneous incompressible Navier-Stokes system with initial density being of the form: $\\eta_1{\\bf 1}_{\\Om_0}+\\eta_2{\\bf 1}_{\\Om_0^c},$ for any pair of positive constants $(\\eta_1,\\eta_2),$ and for any bounded, simply connected $W^{k+2,p}(\\R^2)$ domain $\\Om_0.$ We then prove that the time evolved domain $\\Om(t)$ also belongs to the class of $W^{k+2,p}$ for any $t>"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07922","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"}