{"paper":{"title":"Global well-posedness for the mass-critical stochastic nonlinear Schr\\\"odinger equation on $\\mathbb{R}$: general $L^2$ data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Chenjie Fan, Weijun Xu","submitted_at":"2018-07-12T02:21:06Z","abstract_excerpt":"We continue our study for the stochastic defocusing mass crtical nonlinear Schr\\\"odinger equation with conservative multiplicative noise, and show that it is globally well-posed for arbitrary initial data in $L_{\\omega}^{\\infty}L_{x}^{2}$. The main ingredients are several stability type results for deterministic (modified) NLS, which have their own interest. We also give some results on other stochastic NLS type models."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04402","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"}