{"paper":{"title":"Optimal decay for the $n$-dimensional incompressible Oldroyd-B model without damping mechanism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xiaoping Zhai","submitted_at":"2019-05-07T14:21:49Z","abstract_excerpt":"By a new energy approach involved in the high frequencies and low frequencies decomposition in the Besov spaces, we obtain the optimal decay for the incompressible Oldroyd-B model without damping mechanism in $\\mathbb{R}^n$ ($n\\ge 2$). More precisely, let $(u,\\tau)$ be the global small solutions constructed in [18],\n  we prove for any $(u_0,\\tau_0)\\in{\\dot{B}_{2,1}^{-s}}(\\mathbb{R}^n)$ that \\begin{eqnarray*} \\big\\|\\Lambda^{\\alpha}(u,\\Lambda^{-1}\\mathbb{P}\\mathrm{div}\\tau)\\big\\|_{L^q} \\le C (1+t)^{-\\frac n4-\\frac {(\\alpha+s)q-n}{2q}}, \\quad\\Lambda\\stackrel{\\mathrm{def}}{=}\\sqrt{-\\Delta}, \\end{e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02604","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"}