{"paper":{"title":"Global unique solvability of inhomogeneous Navier-Stokes equations with bounded density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marius Paicu, Ping Zhang, Zhifei Zhang","submitted_at":"2013-01-02T03:15:43Z","abstract_excerpt":"In this paper, we prove the global existence and uniqueness of solution to d-dimensional (for $d=2,3$) incompressible inhomogeneous Navier-Stokes equations with initial density being bounded from above and below by some positive constants, and with initial velocity $u_0\\in H^s(\\R^2)$ for $s>0$ in 2-D, or $u_0\\in H^1(\\R^3)$ satisfying $|u_0|_{L^2}|\\na u_0|_{L^2}$ being sufficiently small in 3-D. This in particular improves the most recent well-posedness result in [10], which requires the initial velocity $u_0\\in H^2(\\R^d)$ for the local well-posedness result, and a smallness condition on the fl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0160","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"}