{"paper":{"title":"Scattering and blowup for $L^{2}$-supercritical and $\\dot{H}^{2}$-subcritical biharmonic NLS with potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hua Wang, Qing Guo, Xiaohua Yao","submitted_at":"2018-10-16T16:06:20Z","abstract_excerpt":"We mainly consider the focusing biharmonic Schr\\\"odinger equation with a large radial repulsive potential $V(x)$: \\begin{equation*} \\left\\{ \\begin{aligned}\n  iu_{t}+(\\Delta^2+V)u-|u|^{p-1}u=0,\\;\\;(t,x) \\in {{\\bf{R}}\\times{\\bf{R}}^{N}},\n  u(0, x)=u_{0}(x)\\in H^{2}({\\bf{R}}^{N}),\n  \\end{aligned}\\right.\n  \\end{equation*} If $N>8$, \\ $1+\\frac{8}{N}<p<1+\\frac{8}{N-4}$ (i.e. the $L^{2}$-supercritical and $\\dot{H}^{2}$-subcritical case ), and $\\langle x\\rangle^\\beta \\big(|V(x)|+|\\nabla V(x)|\\big)\\in L^\\infty$ for some $\\beta>N+4$, then we firstly prove a global well-posedness and scattering result fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07104","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"}