{"paper":{"title":"On the GWP of focusing energy-ciritical inhomogeneous NLS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kiyeon Lee, Seokchang Hong, Yonggeun Cho","submitted_at":"2019-05-24T07:10:59Z","abstract_excerpt":"We consider the focussing energy-critical inhomogeneous nonlinear Schr\\\"odinger equation:\n  $$ iu_t + \\Delta u + g|u|^2u = 0, u(0)= \\varphi \\in \\dot{H}^1,\\;\\; 0 \\le g_i \\le |x|g \\le g_s.$$\n  On the road map of Kenig-Merle \\cite{km} we show the global well-posedness and scattering of radial solutions under energy condition $$E_g(\\varphi) < E_g(Q),\\;\\;\\mbox{and}\\;\\; g_s\\|\\varphi\\|_{\\dot{H}^1}^2 < \\|Q\\|_{\\dot{H}^1}^2,$$ where $Q$ is the solution of $\\Delta Q + |x|^{-1}Q^3 = 0$, together with scaling condition $|g(x)| + |x||\\nabla g(x)| \\lesssim |x|^{-1}$, variational condition $g_s(2-g_i) \\le 1$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10063","kind":"arxiv","version":3},"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"}