{"paper":{"title":"On the local well-posedness of fractionally dissipated primitive equations with transport noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Quyuan Lin, Rongchang Liu, Ruimeng Hu","submitted_at":"2025-01-17T05:09:56Z","abstract_excerpt":"We investigate the three-dimensional fractionally dissipated primitive equations with transport noise, focusing on subcritical and critical dissipation regimes characterized by $ (-\\Delta)^{s/2} $ with $ s \\in (1,2)$ and $s = 1$, respectively. For $\\sigma>3$, we establish the local existence of unique pathwise solutions in Sobolev space $H^\\sigma$. This result applies to arbitrary initial data in the subcritical case ($s \\in(1,2)$), and to small initial data in the critical case ($s=1$). The analysis is particularly challenging due to the loss of horizontal derivatives in the nonlinear terms a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.09956","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/2501.09956/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"}