{"paper":{"title":"On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Noboru Chikami, Rapha\\\"el Danchin","submitted_at":"2014-07-17T13:19:19Z","abstract_excerpt":"We are concerned with the Cauchy problem of the full compressible Navier-Stokes equations satisfied by viscous and heat conducting fluids in $\\mathbb{R}^n.$ We focus on the so-called critical Besov regularity framework. In this setting, it is natural to consider initial densities $\\rho_0,$ velocity fields $u_0$ and temperatures $\\theta_0$ with $a_0:=\\rho_0-1\\in\\dot B^{\\frac np}_{p,1},$ $u_0\\in\\dot B^{\\frac np-1}_{p,1}$ and $\\theta_0\\in\\dot B^{\\frac np-2}_{p,1}.$ After recasting the whole system in Lagrangian coordinates, and working with the \\emph{total energy along the flow} rather than with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4661","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"}