{"paper":{"title":"Random attractors for damped stochastic fractional Schr\\\"odinger equation on $\\mathbb{R}^{n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ao Zhang, Li Lin, Yanjie Zhang","submitted_at":"2024-11-26T06:36:32Z","abstract_excerpt":"We study the random attractors associated with the stochastic fractional Schr\\\"odinger equation on $\\mathbb{R}^n$. Utilizing the stochastic Strichartz estimates for the damped fractional Schr\\\"odinger equation with Gaussian noise, we show the existence and uniqueness of a global solution to the damped stochastic fractional nonlinear Schr\\\"odinger equation in $H^{\\alpha}(\\mathbb{R}^n)$. Furthermore, we demonstrate that this equation defines an infinite-dimensional dynamical system, which possesses a global attractor in $H^{\\alpha}(\\mathbb{R}^n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17151","kind":"arxiv","version":2},"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/2411.17151/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"}