{"paper":{"title":"Scattering in the energy space for the NLS with variable coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Biagio Cassano, Piero D'Ancona","submitted_at":"2015-02-03T17:33:26Z","abstract_excerpt":"We consider the NLS with variable coefficients in dimension $n\\ge3$ \\begin{equation*} i \\partial_t u - Lu +f(u)=0, \\qquad Lv=\\nabla^{b}\\cdot(a(x)\\nabla^{b}v)-c(x)v, \\qquad \\nabla^{b}=\\nabla+ib(x), \\end{equation*} on $\\mathbb{R}^{n}$ or more generally on an exterior domain with Dirichlet boundary conditions, for a gauge invariant, defocusing nonlinearity of power type $f(u)\\simeq|u|^{\\gamma-1}u$. We assume that $L$ is a small, long range perturbation of $\\Delta$, plus a potential with a large positive part. The first main result of the paper is a bilinear smoothing (interaction Morawetz) estima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00937","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"}