{"paper":{"title":"Sharp decay characterization for the incompressible Oldroyd-B model in critical $L^p$ spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"An L2-type low-frequency condition on initial data is almost necessary and sufficient for optimal upper and lower bounds on temporal decay of solutions to the incompressible Oldroyd-B model without viscosity or damping in critical Besov spaces.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiahong Wu, Lvqiao Liu, Mingwen Fei, Zhi Chen","submitted_at":"2026-05-13T14:33:17Z","abstract_excerpt":"This paper establishes a sharp characterization of temporal decay rates for the incompressible Oldroyd-B model in a critical $L^p$ framework, covering the physically relevant and mathematically delicate case where both the fluid viscosity and the stress tensor damping are absent. We prove that an $L^2$-type condition on the low-frequencies part of the initial data $(u_0, \\tau_0)$ is almost both necessary and sufficient for obtaining optimal upper and lower bounds on the temporal decay of solutions in critical Besov spaces. A key contribution is a new decomposition of the stress tensor into its"},"claims":{"count":3,"items":[{"kind":"strongest_claim","text":"an L^2-type condition on the low-frequencies part of the initial data (u_0, τ_0) is almost both necessary and sufficient for obtaining optimal upper and lower bounds on the temporal decay of solutions in critical Besov spaces","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The new decomposition of the stress tensor into incompressible and compressible parts together with the effective tensor successfully controls the loss of regularity in high-frequency velocity without introducing uncontrolled errors or extra assumptions on the data.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"An L2-type low-frequency condition on initial data is almost necessary and sufficient for optimal upper and lower bounds on temporal decay of solutions to the incompressible Oldroyd-B model without viscosity or damping in critical Besov spaces.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"}],"snapshot_sha256":"a1a5ba691e0a9fd77ff6b54c00413165f9e0d3f0443b9ff8dadd876ecb287bd4"},"source":{"id":"2605.13598","kind":"arxiv","version":1},"verdict":{"id":"a57eb71a-45bd-499f-bbe8-2250bce3d0a7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T17:51:01.785838Z","strongest_claim":"an L^2-type condition on the low-frequencies part of the initial data (u_0, τ_0) is almost both necessary and sufficient for obtaining optimal upper and lower bounds on the temporal decay of solutions in critical Besov spaces","one_line_summary":"An L2-type low-frequency condition on initial data is almost necessary and sufficient for optimal upper and lower bounds on temporal decay of solutions to the incompressible Oldroyd-B model without viscosity or damping in critical Besov spaces.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The new decomposition of the stress tensor into incompressible and compressible parts together with the effective tensor successfully controls the loss of regularity in high-frequency velocity without introducing uncontrolled errors or extra assumptions on the data.","pith_extraction_headline":""},"references":{"count":40,"sample":[{"doi":"","year":2011,"title":"H. Bahouri, J.-Y. Chemin, and R. Danchin.Fourier analysis and nonlinear partial differ- ential equations, volume 343 ofGrundlehren der mathematischen Wissenschaften [Fun- damental Principles of Mathem","work_id":"4904dd17-89c0-4253-a2e1-d1f201b3ecad","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"J. W. Barrett and S. Boyaval. Existence and approximation of a (regularized) Oldroyd-B model.Math. Models Methods Appl. Sci., 21(9):1783–1837, 2011","work_id":"4ba7afc7-64f7-42e2-8443-a20bc83587d2","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"L. Brandolese. Characterization of solutions to dissipative systems with sharp algebraic decay.SIAM J. Math. Anal., 48(3):1616–1633, 2016. 48 ZHI CHEN, MINGWEN FEI, L VQIAO LIU, AND JIAHONG WU","work_id":"3d4d3265-d299-4550-953c-18bf176488a9","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"L. Brandolese, L.-Y. Shou, J. Xu, and P. Zhang. Sharp decay characterization for the compressible Navier-Stokes equations.Adv. Math., 456:Paper No. 109905, 60, 2024","work_id":"c1d2e092-0fe0-4791-ae51-2fc1846ff36a","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1978,"title":"M. G. Brereton. Dynamics of polymeric liquids.Physics Bulletin, 29(1):26, 1978","work_id":"b08023ca-3ba9-4956-b78b-816336ab215b","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":40,"snapshot_sha256":"686b845f87a6f543236443bb2f571263c505e82a5ed95a9482fe1ec086833650","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"}