Long time inviscid damping near Couette in Sobolev spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912730883031040 |
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| author | Guo, Dengjun Luo, Xiaoyutao |
| author_facet | Guo, Dengjun Luo, Xiaoyutao |
| contents | We give an elementary proof of long time inviscid damping for Sobolev perturbations near the Couette flow $(y,0)$ for the 2D Euler equations on $\mathbb{T} \times \mathbb{R}$. For any $s>1$ and any initial vorticity perturbation of size $O(ε)$ in $H^s$, we obtain velocity damping estimates up to a time scale $ t = O(ε^{-δ_s} )$, where $δ_s=1/3$ when $s\to 1+$ and $δ_s=1/2$ for $s>2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21583 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long time inviscid damping near Couette in Sobolev spaces Guo, Dengjun Luo, Xiaoyutao Analysis of PDEs We give an elementary proof of long time inviscid damping for Sobolev perturbations near the Couette flow $(y,0)$ for the 2D Euler equations on $\mathbb{T} \times \mathbb{R}$. For any $s>1$ and any initial vorticity perturbation of size $O(ε)$ in $H^s$, we obtain velocity damping estimates up to a time scale $ t = O(ε^{-δ_s} )$, where $δ_s=1/3$ when $s\to 1+$ and $δ_s=1/2$ for $s>2$. |
| title | Long time inviscid damping near Couette in Sobolev spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.21583 |