{"paper":{"title":"Optimal well-posedness for the inhomogeneous incompressible Navier-Stokes system with general viscosity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cosmin Burtea","submitted_at":"2016-08-08T10:53:28Z","abstract_excerpt":"In this paper we obtain new well-possedness results concerning a linear inhomogenous Stokes-like system. These results are used to establish local well-posedness in the critical spaces for initial density $\\rho_{0}$ and velocity $u_{0}$ such that $\\rho_{0}-\\rho\\in\\dot{B}_{p,1}^{\\frac{3}{p}}(\\mathbb{R}^{3})$, $u_{0}\\in\\dot{B}_{p,1}^{\\frac{3}{p}-1}(\\mathbb{R}^{3})$, $p\\in\\left( \\frac{6}{5},4\\right) $, for the inhomogeneous incompressible Navier-Stokes system with variable viscosity. To the best of our knowledge, regarding the $3D$ case, this is the first result in a truly critical framework for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02378","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"}