Parabolic-scalings on large-time behavior of the incompressible Navier--Stokes flow
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916721248436224 |
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| author | Yamamoto, Masakazu |
| author_facet | Yamamoto, Masakazu |
| contents | Through asymptotic expansion, the large-time behavior of incompressible Navier--Stokes flow in $n$-dimensional whole space is depicted. Especially, from their parabolic scalings, large-time behaviors of any terms on the expansion are clarified. The parabolic scalings also guarantee the uniqueness of the expansion. In the preceding work, the expansion with the $n$th order has already been derived. They also predicted that the flow has some logarithmic evolutions in higher-order decay. In this paper, an asymptotic expansion with $2n$th order is presented. Furthermore, logarithmic evolutions are discovered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18452 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parabolic-scalings on large-time behavior of the incompressible Navier--Stokes flow Yamamoto, Masakazu Analysis of PDEs 35Q30 35B40 35C20 76C05 Through asymptotic expansion, the large-time behavior of incompressible Navier--Stokes flow in $n$-dimensional whole space is depicted. Especially, from their parabolic scalings, large-time behaviors of any terms on the expansion are clarified. The parabolic scalings also guarantee the uniqueness of the expansion. In the preceding work, the expansion with the $n$th order has already been derived. They also predicted that the flow has some logarithmic evolutions in higher-order decay. In this paper, an asymptotic expansion with $2n$th order is presented. Furthermore, logarithmic evolutions are discovered. |
| title | Parabolic-scalings on large-time behavior of the incompressible Navier--Stokes flow |
| topic | Analysis of PDEs 35Q30 35B40 35C20 76C05 |
| url | https://arxiv.org/abs/2410.18452 |