{"paper":{"title":"Lower bound for the rate of blow-up of singular solutions of the Zakharov system in $\\R^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"C. Sulem, J. Colliander, M. Czubak","submitted_at":"2013-05-02T01:33:48Z","abstract_excerpt":"We consider the scalar Zakharov system in $\\R^3$ for initial conditions $(\\psi(0), n(0), n_t(0)) \\in H^{\\ell+1/2} \\times H^\\ell \\times H^{\\ell-1} $,\n  $0\\leq\\ell \\leq 1$. Assuming that the solution blows up in a finite time $t^* < \\infty$, we establish a lower bound for the rate of blow-up of the corresponding Sobolev norms in the form $$ \\|\\psi(t)\\|_{H^{\\ell+1/2}} +\\|n(t)\\|_{H^{\\ell}} + \\|n_t(t)\\|_{H^{\\ell-1}} > C(t^*-t)^{-\\theta_\\ell} $$ with $\\theta_\\ell = \\frac{1}{4}(1+ 2 \\ell)^-$. The analysis is a reappraisal of the local wellposedness theory of Ginibre, Tsutsumi and Velo (1997) combined"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0324","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"}