{"paper":{"title":"Local/global well-posedness analysis of time-space fractional Schr\\\"{o}dinger equation on $\\mathbb{R}^{d}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yong Zhen Yang, Yong Zhou","submitted_at":"2025-07-06T14:55:25Z","abstract_excerpt":"We investigate a class of nonlinear time-space fractional Schr\\\"{o}dinger equations with nonlocal effects in both time and space. The time derivative is of Achar type, and the space operator is a $\\phi(-\\Delta)$-type operator defined via a Bernstein function $\\phi$. This nonlocality invalidates classical Strichartz estimates. By combining asymptotic analysis of Mittag-Leffler functions, the H\\\"{o}rmander multiplier theorem, and harmonic analysis techniques, we establish a Gagliardo-Nirenberg inequality in $\\phi$-Triebel-Lizorkin spaces and derive key Sobolev estimates for the solution operator"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04411","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/2507.04411/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"}