{"paper":{"title":"Long-time dynamics for time-nonlocal generalized Rayleigh-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Nonlocal time-fractional evolution equations generate a semi-dynamical system with an attracting set and attractors in a suitable weighted function space under dissipativity and local Lipschitz conditions.","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jia Wei He, Lin Deng, Li Peng","submitted_at":"2026-05-11T11:55:49Z","abstract_excerpt":"In this paper, we consider an autonomous semi-dynamical system driven by semilinear time-nonlocal evolution equations, these type equations are used to describe the Rayleigh-Stokes problem for a non-Newtonain fluid to a generalized second grade fluid. We first investigate the global well-posedness of solutions consisting of global Lipschitz condition by a weighted space $\\mathcal C$. Utilizing the topology convergence on compact subsets of $\\mathcal C$, we construct a semi-dynamical system that satisfies the semi-group structure. It also is shown that this semi-dynamical system has an attracti"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"It also is shown that this semi-dynamical system has an attracting set in C_ρ when the vector field function satisfies a dissipativity condition as well as a local Lipschitz condition. With the compactness, we also get the existence of attractors.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The vector field function satisfies a dissipativity condition as well as a local Lipschitz condition (invoked to obtain the attracting set in C_ρ).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Existence of an attracting set and attractors is established for a semi-dynamical system generated by time-nonlocal generalized Rayleigh-Stokes equations in the space C_ρ under dissipativity and local Lipschitz assumptions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Nonlocal time-fractional evolution equations generate a semi-dynamical system with an attracting set and attractors in a suitable weighted function space under dissipativity and local Lipschitz conditions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"439e32ce0633584af886699d20cc5feb2a7cdcf30ed81475d3f989bf9423adfb"},"source":{"id":"2605.10421","kind":"arxiv","version":2},"verdict":{"id":"578202c6-7a43-4737-a3a1-5ebb86e74a49","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T05:14:29.115268Z","strongest_claim":"It also is shown that this semi-dynamical system has an attracting set in C_ρ when the vector field function satisfies a dissipativity condition as well as a local Lipschitz condition. With the compactness, we also get the existence of attractors.","one_line_summary":"Existence of an attracting set and attractors is established for a semi-dynamical system generated by time-nonlocal generalized Rayleigh-Stokes equations in the space C_ρ under dissipativity and local Lipschitz assumptions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The vector field function satisfies a dissipativity condition as well as a local Lipschitz condition (invoked to obtain the attracting set in C_ρ).","pith_extraction_headline":"Nonlocal time-fractional evolution equations generate a semi-dynamical system with an attracting set and attractors in a suitable weighted function space under dissipativity and local Lipschitz conditions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.10421/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T15:33:39.452597Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T11:31:18.017614Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T09:21:49.352352Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"7d6d7cb1ee8866a5adf4cda23dd5120f69fceb28003f050e4ba64d2642856066"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"e0e26ccd999ac4c459455cd9a690a1de26eef72a5f2489f2724ad8de30d5fe27"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}