{"paper":{"title":"Energy critical Schr\\\"odinger equation with weighted exponential nonlinearity I: Local and global well-posedness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelwahab Bensouilah, Dhouha Draouil, Mohamed Majdoub","submitted_at":"2017-10-17T19:16:51Z","abstract_excerpt":"We investigate the initial value problem for a defocusing nonlinear Schr\\\"odinger equation with weighted exponential nonlinearity $$ i\\partial_t u+\\Delta u=\\frac{u}{|x|^b}(e^{\\alpha|u|^2}-1); \\qquad (t,x) \\in \\mathbb{R}\\times\\mathbb{R}^2, $$ where $0< b <1$ and $\\alpha=2\\pi(2-b)$. We establish local and global well-posedness in the subcritical and critical regimes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06477","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"}