The stability threshold for 2D MHD equations around Couette with general viscosity and magnetic resistivity
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917819190345728 |
|---|---|
| author | Wang, Fei Zhang, Zeren |
| author_facet | Wang, Fei Zhang, Zeren |
| contents | We address a threshold problem of the Couette flow $(y,0)$ in a uniform magnetic field $(β,0)$ for the 2D MHD equation on $\mathbb{T}\times\mathbb{R}$ with fluid viscosity $ν$ and magnetic resistivity $μ$. The nonlinear enhanced dissipation and inviscid damping are also established. In particularly, when $0<ν\leqμ^3\leq1$, we get a threshold $ν^{\frac{1}{2}}μ^{\frac{1}{3}}$ in $H^N(N\geq4)$. When $0<μ^3\leqν\leq1$, we obtain a threshold $\min\{ν^{\frac{1}{2}},μ^{\frac{1}{2}}\}\min\{1,ν^{-1}μ^{\frac{1}{3}}\}$, hence improving the results in [19,14,21]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20404 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The stability threshold for 2D MHD equations around Couette with general viscosity and magnetic resistivity Wang, Fei Zhang, Zeren Analysis of PDEs We address a threshold problem of the Couette flow $(y,0)$ in a uniform magnetic field $(β,0)$ for the 2D MHD equation on $\mathbb{T}\times\mathbb{R}$ with fluid viscosity $ν$ and magnetic resistivity $μ$. The nonlinear enhanced dissipation and inviscid damping are also established. In particularly, when $0<ν\leqμ^3\leq1$, we get a threshold $ν^{\frac{1}{2}}μ^{\frac{1}{3}}$ in $H^N(N\geq4)$. When $0<μ^3\leqν\leq1$, we obtain a threshold $\min\{ν^{\frac{1}{2}},μ^{\frac{1}{2}}\}\min\{1,ν^{-1}μ^{\frac{1}{3}}\}$, hence improving the results in [19,14,21]. |
| title | The stability threshold for 2D MHD equations around Couette with general viscosity and magnetic resistivity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.20404 |