{"paper":{"title":"Time-periodic solutions of the Vlasov-Poisson-Boltzmann system with a general external force in $\\mathbb{R}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Jinkai Ni, Renjun Duan","submitted_at":"2026-08-06T06:25:03Z","abstract_excerpt":"In this paper, we study the time-periodic problem for the Vlasov-Poisson-Boltzmann (VPB) system with a given time-periodic external force in the whole space $\\mathbb{R}^3$. The force is allowed to be non-potential. Around the global Maxwellian, we prove the global existence of small solutions in a hybrid function space that combines the low-frequency Besov framework for the forced Boltzmann equation with a corresponding control of the self-consistent electric field. The main novelty lies in the treatment of the nonlinear Vlasov force $-\\nabla_x\\phi \\cdot \\nabla_vf + \\frac{1}{2}(v \\cdot \\nabla_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05637","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/2608.05637/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"}