Transition Threshold for Strictly Monotone Shear Flows in Sobolev Spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916497806327808 |
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| author | Beekie, Rajendra He, Siming |
| author_facet | Beekie, Rajendra He, Siming |
| contents | We study the stability of spectrally stable, strictly monotone, smooth shear flows in the 2D Navier-Stokes equations on $\mathbb{T} \times \mathbb{R}$ with small viscosity $ν$. We establish nonlinear stability in $H^s$ for $s \geq 2$ with a threshold of size $εν^{1/3}$ for time smaller than $c_*ν^{-1}$ with $ε, c_* \ll 1$. Additionally, we demonstrate nonlinear inviscid damping and enhanced dissipation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09219 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transition Threshold for Strictly Monotone Shear Flows in Sobolev Spaces Beekie, Rajendra He, Siming Analysis of PDEs We study the stability of spectrally stable, strictly monotone, smooth shear flows in the 2D Navier-Stokes equations on $\mathbb{T} \times \mathbb{R}$ with small viscosity $ν$. We establish nonlinear stability in $H^s$ for $s \geq 2$ with a threshold of size $εν^{1/3}$ for time smaller than $c_*ν^{-1}$ with $ε, c_* \ll 1$. Additionally, we demonstrate nonlinear inviscid damping and enhanced dissipation. |
| title | Transition Threshold for Strictly Monotone Shear Flows in Sobolev Spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.09219 |