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arXiv · 2512.22921

Diffusion wave phenomena and optimal time decay for incompressible viscoelastic flows

Shenghan Li·Yong Wang
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Abstract

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.

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Shenghan Li, Yong Wang. 2025-12-28. Diffusion wave phenomena and optimal time decay for incompressible viscoelastic flows. https://arxiv.org/abs/2512.22921

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