{"paper":{"title":"Exponential stability for the three-dimensional Navier-Stokes equations on negatively curved manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.DG","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Samuel L. Braunstein, Zhi-Wei Wang","submitted_at":"2026-06-03T03:35:34Z","abstract_excerpt":"We extend the exponential stability theorem for the three-dimensional incompressible Navier-Stokes equations from hyperbolic 3-space $\\HH^3$ (established in a companion paper) to complete simply connected Riemannian 3-manifolds $(M^3, g)$ with pinched negative sectional curvature $-b^2 \\leq K \\leq -a^2 < 0$ and bounded geometry (including a strictly positive injectivity radius). The deformation Laplacian $\\Delta_\\Def = \\Delta_B + \\Ric$ remains the viscous operator, selected by Lagrangian kinematics. We prove that the {exact} system admits a unique global mild solution for small $L^3$ data, wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04407","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/2606.04407/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"}