{"paper":{"title":"On the scattering problem for the nonlinear Schr\\\"{o}dinger equation with a potential in 2D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chunhua Li, Vladimir Georgiev","submitted_at":"2018-12-31T12:52:10Z","abstract_excerpt":"We consider the scattering problem for the nonlinear Schr\\\"{o}dinger equation with a potential in two space dimensions. Appropriate resolvent estimates are proved and applied to estimate the operator $A(s)$ appearing in commutator relations. The equivalence between the operators $\\left(-\\Delta_{V}\\right)^{\\frac{s}{2}}$ and $\\left(-\\Delta \\right)^{\\frac{s}{2}}$ in $L^{2}$ norm sense for $0\\leq s <1$ is investigated by using free resolvent estimates and Gaussian estimates for the heat kernel of the Schr\\\"{o}dinger operator $-\\Delta_{V}$. Our main result guarantees the global existence of solutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11777","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"}