{"paper":{"title":"Entropy Structures and Long-Time Relaxation for 3-Wave Kinetic Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A one-sided algebraic balance condition on interaction weights generates new entropy structures that produce global weak L1_loc solutions to three-wave kinetic equations and force local relaxation to zero as time tends to infinity.","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Gigliola Staffilani, Minh-Binh Tran","submitted_at":"2026-05-11T16:20:59Z","abstract_excerpt":"We establish a new class of entropy structures for \\(3\\)-wave kinetic equations with a broad family of interaction weights. Unlike the classical entropies arising from detailed balance, these estimates are generated by a one-sided algebraic balance condition encoded in the interaction weights. To the best of our knowledge, this family of entropy estimates has not previously appeared in the physical literature on wave turbulence. These estimates form the central a priori mechanism of the paper and are the key ingredient in the construction of global weak \\(L^1_{\\mathrm{loc}}\\) solutions. We als"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish a new class of entropy structures for 3-wave kinetic equations with a broad family of interaction weights. ... these estimates form the central a priori mechanism of the paper and are the key ingredient in the construction of global weak L1_loc solutions. We also prove a long-time rigidity result, showing that the solutions obtained by this entropy compactness method relax locally to the zero equilibrium as t→∞.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The interaction weights satisfy a one-sided algebraic balance condition that is sufficient to generate the new entropy structures and close the estimates.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"New entropy structures from one-sided balance conditions on interaction weights yield global weak L1_loc solutions to 3-wave kinetic equations and prove their local relaxation to zero equilibrium.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A one-sided algebraic balance condition on interaction weights generates new entropy structures that produce global weak L1_loc solutions to three-wave kinetic equations and force local relaxation to zero as time tends to infinity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"bb5cc3170afd02802e2f328ad89116a0fa44a713e6aa4fe722e0e63f2d6050f9"},"source":{"id":"2605.10788","kind":"arxiv","version":2},"verdict":{"id":"16339132-07e3-4ea4-8754-077a49fb260f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T03:57:28.624401Z","strongest_claim":"We establish a new class of entropy structures for 3-wave kinetic equations with a broad family of interaction weights. ... these estimates form the central a priori mechanism of the paper and are the key ingredient in the construction of global weak L1_loc solutions. We also prove a long-time rigidity result, showing that the solutions obtained by this entropy compactness method relax locally to the zero equilibrium as t→∞.","one_line_summary":"New entropy structures from one-sided balance conditions on interaction weights yield global weak L1_loc solutions to 3-wave kinetic equations and prove their local relaxation to zero equilibrium.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The interaction weights satisfy a one-sided algebraic balance condition that is sufficient to generate the new entropy structures and close the estimates.","pith_extraction_headline":"A one-sided algebraic balance condition on interaction weights generates new entropy structures that produce global weak L1_loc solutions to three-wave kinetic equations and force local relaxation to zero as time tends to infinity."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.10788/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T05:22:00.382065Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T14:35:50.992508Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T10:31:17.786531Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T08:58:52.013508Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"8a49d461d5c5345906aeb03164dcb59bdd741cabe0c0871538a845636c32727b"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"169a60b8763f51ed7b9ba10a6c167e4eed455e12ec1b8eff5fa4237fefbe3193"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}