Diffusion wave phenomena and optimal time decay for incompressible viscoelastic flows
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911341457965056 |
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| author | Li, Shenghan Wang, Yong |
| author_facet | Li, Shenghan Wang, Yong |
| contents | Motivated by the work of D. Hoff and K. Zumbrun (Indiana Univ. Math. J. 44: 603-676, 1995), we investigate the diffusion wave phenomena in three-dimensional incompressible viscoelastic flows. By employing the representation formula of the wave equation and the stationary phase methods on the sphere $\mathbb{S}^{d-1}$, we establish $L^p$ decay estimates for the solution over the whole range $1\leq p \leq \infty$, which reveals the hyperbolic nature of the incompressible viscoelastic flows. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_22921 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diffusion wave phenomena and optimal time decay for incompressible viscoelastic flows Li, Shenghan Wang, Yong Analysis of PDEs Motivated by the work of D. Hoff and K. Zumbrun (Indiana Univ. Math. J. 44: 603-676, 1995), we investigate the diffusion wave phenomena in three-dimensional incompressible viscoelastic flows. By employing the representation formula of the wave equation and the stationary phase methods on the sphere $\mathbb{S}^{d-1}$, we establish $L^p$ decay estimates for the solution over the whole range $1\leq p \leq \infty$, which reveals the hyperbolic nature of the incompressible viscoelastic flows. |
| title | Diffusion wave phenomena and optimal time decay for incompressible viscoelastic flows |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.22921 |