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arXiv · 2408.15586

Decay Rates for Viscous Surface Waves of Isotropic Micropolar Fluids With or Without Surface Tension

Yuchong Wei·Zheng-an Yao
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Abstract

In this paper, we consider a layer of viscous incompressible isotropic micropolar fluid in a uniform gravitational field of finite depth, lying above a flat rigid bottom and below the atmosphere in a three-dimensional horizontally periodic setting. The fluid dynamics are governed by gravity-driven incompressible micropolar equations. We investigate the global well-posedness for both the cases with and without surface tension. On one hand, in the case with surface tension (i.e. {\sigma} > 0), we show that the global solution decays to the equilibrium exponentially. On the other hand, in the case without surface tension (i.e. {\sigma} = 0), the solution decays to the equilibrium at an almost exponential rate. Comparing the two different cases for {\sigma} > 0 and {\sigma} = 0 reveals that the surface tension can enhance the decay rate.

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Yuchong Wei, Zheng-an Yao. 2024-08-28. Decay Rates for Viscous Surface Waves of Isotropic Micropolar Fluids With or Without Surface Tension. https://arxiv.org/abs/2408.15586

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