{"paper":{"title":"Blow-up for the 1D nonlinear Schr\\\"odinger equation with point nonlinearity I: Basic theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chang Liu, Justin Holmer","submitted_at":"2015-10-13T00:41:33Z","abstract_excerpt":"We consider the 1D nonlinear Schr\\\"odinger equation (NLS) with focusing point nonlinearity, $$ (\\delta\\text{NLS}) \\qquad i\\partial_t\\psi + \\partial_x^2\\psi + \\delta|\\psi|^{p-1}\\psi = 0, $$ where $\\delta=\\delta(x)$ is the delta function supported at the origin. We show that $\\delta$NLS shares many properties in common with those previously established for the focusing autonomous translationally-invariant NLS $$ (\\text{NLS}) \\qquad i\\partial_t \\psi + \\Delta \\psi + |\\psi|^{p-1}\\psi=0 \\,. $$ The critical Sobolev space $\\dot H^{\\sigma_c}$ for $\\delta$NLS is $\\sigma_c=\\frac12-\\frac{1}{p-1}$, whereas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03491","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"}