{"paper":{"title":"Global well-posedness of 3-D inhomogeneous Navier-Stokes equations with ill-prepared initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ping Zhang, Zhifei Zhang","submitted_at":"2014-09-05T02:56:17Z","abstract_excerpt":"In this paper, we investigate the global well-posedness of 3-D incompressible inhomogeneous Navier-Stokes equations with ill-prepared large initial data which are slowly varying in one space variable, that is, initial data of the form $\\bigl(1+\\e^{\\be}a_0(x_{\\rm h},\\e x_3),(\\ve^{1-\\al} v^{\\rm h}_0, \\ve^{-\\al}v_0^3)(x_{\\rm h},\\e x_3)\\bigr)$ for any $\\al\\in ]0,1/3[,$\n  $\\be>2\\al,$ and $\\ve$ being sufficiently small. We remark that initial data of this type do not satisfy the smallness conditions in \\cite{c-p-z,HPZ3} no matter how small $\\e$ is. In particular, this result greatly improves the glo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1649","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"}