{"paper":{"title":"Non-Smooth Solutions of the Navier-Stokes Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Non-smooth Leray-Hopf solutions to the Navier-Stokes equations are constructed and blow up in finite time.","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"J. Glimm, J. Petrillo","submitted_at":"2024-10-11T21:25:05Z","abstract_excerpt":"Non-smooth Leray-Hopf solutions of the Navier-Stokes equation are constructed. The construction occurs in a finite periodic cube T3. Entropy production maximizing solutions with turbulent initial data are selected. The proof of finite time blowup is based on analyticity properties of the weak solutions of the Navier-Stokes equation. The turbulent initial data is characterized in terms of its expansion in spherical harmonics basis functions. The mean value of a weak solution of the Navier-Stokes equation is identified as a smooth solution of the Navier-Stokes equation"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Non-smooth Leray-Hopf solutions of the Navier-Stokes equation are constructed. The proof of finite time blowup is based on analyticity properties of the weak solutions of the Navier-Stokes equation. The turbulent initial data is characterized in terms of its expansion in spherical harmonics basis functions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The selection of entropy production maximizing solutions with turbulent initial data, characterized via spherical harmonics expansion, produces non-smooth behavior whose finite-time blowup follows from analyticity properties of weak solutions (abstract, no further specification of the analyticity argument or the entropy functional).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Constructs non-smooth Leray-Hopf weak solutions to 3D Navier-Stokes in periodic cube T3 with finite-time blowup, using entropy-maximizing turbulent initial data expanded in spherical harmonics; mean value is smooth.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Non-smooth Leray-Hopf solutions to the Navier-Stokes equations are constructed and blow up in finite time.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"fcbc4f0d42729cf3fbe68d245c5158c8e47864c940efdef43a3f3ebed75e1762"},"source":{"id":"2410.09261","kind":"arxiv","version":8},"verdict":{"id":"25ed33e0-8812-4476-ae7d-6fd07a364bba","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-23T18:58:10.773343Z","strongest_claim":"Non-smooth Leray-Hopf solutions of the Navier-Stokes equation are constructed. The proof of finite time blowup is based on analyticity properties of the weak solutions of the Navier-Stokes equation. The turbulent initial data is characterized in terms of its expansion in spherical harmonics basis functions.","one_line_summary":"Constructs non-smooth Leray-Hopf weak solutions to 3D Navier-Stokes in periodic cube T3 with finite-time blowup, using entropy-maximizing turbulent initial data expanded in spherical harmonics; mean value is smooth.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The selection of entropy production maximizing solutions with turbulent initial data, characterized via spherical harmonics expansion, produces non-smooth behavior whose finite-time blowup follows from analyticity properties of weak solutions (abstract, no further specification of the analyticity argument or the entropy functional).","pith_extraction_headline":"Non-smooth Leray-Hopf solutions to the Navier-Stokes equations are constructed and blow up in finite time."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.09261/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":2,"snapshot_sha256":"8e81ab6a5727c00b8decd2beb098c75e216cd8b62209516a6ab580c6c1c1d2c0"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}