{"paper":{"title":"Damped nonlinear Schr\\\"odinger equation with Stark effect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shijun Zheng, Yi Hu, Yongki Lee","submitted_at":"2023-06-09T14:45:44Z","abstract_excerpt":"We study the $L^2$-critical damped NLS with a Stark potential. We prove that the threshold for global existence and finite time blowup of this equation is given by $\\|Q\\|_2$, where $Q$ is the unique positive radial solution of $\\Delta Q + |Q|^{4/d} Q = Q$ in $H^1(\\mathbb{R}^d)$. Moreover, in any small neighborhood of $Q$, there exists an initial data $u_0$ above the ground state such that the solution flow admits the log-log blowup speed. This verifies the structural stability for the ``$\\log$-$\\log$ law'' associated to the NLS mechanism under the perturbation by a damping term and a Stark pot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.05931","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.05931/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}