Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.15586 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 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. σ > 0), we show that the global solution decays to the equilibrium exponentially. On the other hand, in the case without surface tension (i.e. σ = 0), the solution decays to the equilibrium at an almost exponential rate. Comparing the two different cases for σ > 0 and σ = 0 reveals that the surface tension can enhance the decay rate.