{"paper":{"title":"Orbital stability of normalized ground states for critical Choquard equation with potential","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jun Wang, Zhaoyang Yin","submitted_at":"2024-12-11T15:52:43Z","abstract_excerpt":"In this paper, we study the existence of ground state standing waves and orbital stability, of prescribed mass, for the nonlinear critical Choquard equation \\begin{equation*}\n  \\left\\{\\begin{array}{l} i \\partial_t u+\\Delta u -V(x)u+(I_{\\alpha}\\ast|u|^{q})|u|^{q-2}u+(I_{\\alpha}\\ast|u|^{2_{\\alpha}^*})|u|^{2_{\\alpha}^*-2}u=0,\\ (x, t) \\in \\mathbb{R}^d \\times \\mathbb{R}, \\\\ \\left.u\\right|_{t=0}=\\varphi \\in H ^1(\\mathbb{R}^d), \\end{array}\\right. \\end{equation*} where $I_{\\alpha}$ is a Riesz potential of order $\\alpha\\in(0,d),\\ d\\geq3,\\ 2_{\\alpha}^*=\\frac{2d-\\alpha}{d-2}$ is the upper critical expone"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.08488","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/2412.08488/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"}