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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2105.00730 |
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| _version_ | 1866913307682668544 |
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| author | Chen, Zhi-Min |
| author_facet | Chen, Zhi-Min |
| contents | In the present study, Kolmogorov flow represents the stationary sinusoidal solution $(\sin y,0)$ to a two-dimensional spatially periodic Navier-Stokes system, driven by an external force. This system admits the additional non-stationary solution $(\sin y,0)+e^{-νt} (\sin y,0)$, which tends exponentially to the Kolmogorov flow at the minimum decay rate determined by the viscosity $ν$. Enhanced damping or enhanced dissipation of the problem is obtained by presenting higher decay rate for the difference between a solution and the non-stationary basic solution. Moreover, for the understanding of the metastability problem in an explicit manner, a variety of exact solutions are presented to show enhanced and unenhanced dampings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_00730 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Enhanced and unenhanced dampings of the Kolmogorov flow Chen, Zhi-Min Analysis of PDEs In the present study, Kolmogorov flow represents the stationary sinusoidal solution $(\sin y,0)$ to a two-dimensional spatially periodic Navier-Stokes system, driven by an external force. This system admits the additional non-stationary solution $(\sin y,0)+e^{-νt} (\sin y,0)$, which tends exponentially to the Kolmogorov flow at the minimum decay rate determined by the viscosity $ν$. Enhanced damping or enhanced dissipation of the problem is obtained by presenting higher decay rate for the difference between a solution and the non-stationary basic solution. Moreover, for the understanding of the metastability problem in an explicit manner, a variety of exact solutions are presented to show enhanced and unenhanced dampings. |
| title | Enhanced and unenhanced dampings of the Kolmogorov flow |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2105.00730 |