Sobolev Stability for the 2D MHD Equations in the Non-Resistive Limit
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929219843391488 |
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| author | Knobel, Niklas |
| author_facet | Knobel, Niklas |
| contents | In this article, we consider the stability of the 2D magnetohydrodynamics (MHD) equations close to a combination of Couette flow and a constant magnetic field. We consider the ideal conductor limit for the case when viscosity $ν$ is larger than resistivity $κ$, $ν\ge κ>0$. For this regime, we establish a bound on the Sobolev stability threshold. Furthermore, for $κ\le ν^3$ this system exhibits instability, which leads to norm inflation of size $νκ^{-\frac 1 3 }$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12548 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sobolev Stability for the 2D MHD Equations in the Non-Resistive Limit Knobel, Niklas Analysis of PDEs Mathematical Physics In this article, we consider the stability of the 2D magnetohydrodynamics (MHD) equations close to a combination of Couette flow and a constant magnetic field. We consider the ideal conductor limit for the case when viscosity $ν$ is larger than resistivity $κ$, $ν\ge κ>0$. For this regime, we establish a bound on the Sobolev stability threshold. Furthermore, for $κ\le ν^3$ this system exhibits instability, which leads to norm inflation of size $νκ^{-\frac 1 3 }$. |
| title | Sobolev Stability for the 2D MHD Equations in the Non-Resistive Limit |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2401.12548 |