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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2605.13598 |
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| _version_ | 1866917491592134656 |
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| author | Chen, Zhi Fei, Mingwen Liu, Lvqiao Wu, Jiahong |
| author_facet | Chen, Zhi Fei, Mingwen Liu, Lvqiao Wu, Jiahong |
| contents | 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 $(u_0, τ_0)$ is almost both necessary and sufficient for obtaining optimal upper and lower bounds on the temporal decay of solutions in critical Besov spaces. A key contribution is a new decomposition of the stress tensor into its incompressible and compressible parts, combined with the introduction of an effective tensor to handle the loss of regularity in the high-frequencies velocity field. This is the first result to reveal such precise two-sided asymptotics for the incompressible Oldroyd-B model without viscosity or damping. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13598 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp decay characterization for the incompressible Oldroyd-B model in critical $L^p$ spaces Chen, Zhi Fei, Mingwen Liu, Lvqiao Wu, Jiahong Analysis of PDEs 35Q35 35B40 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 $(u_0, τ_0)$ is almost both necessary and sufficient for obtaining optimal upper and lower bounds on the temporal decay of solutions in critical Besov spaces. A key contribution is a new decomposition of the stress tensor into its incompressible and compressible parts, combined with the introduction of an effective tensor to handle the loss of regularity in the high-frequencies velocity field. This is the first result to reveal such precise two-sided asymptotics for the incompressible Oldroyd-B model without viscosity or damping. |
| title | Sharp decay characterization for the incompressible Oldroyd-B model in critical $L^p$ spaces |
| topic | Analysis of PDEs 35Q35 35B40 |
| url | https://arxiv.org/abs/2605.13598 |