Sobolev stability for the 2D MHD equations in the non-resistive limit
Abstract:
In this article, we consider the stability of the 2D magnetohydrodynamics
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 ⩾ κ > 0. For this regime, we establish a bound on
the Sobolev stability threshold. Furthermore, for κ ⩽ ν$^3$ this system exhibits
instability, which leads to norm inflation of size νκ$^{−\frac{1}{3}}$ .
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 ⩾ κ > 0. For this regime, we establish a bound on
the Sobolev stability threshold. Furthermore, for κ ⩽ ν$^3$ this system exhibits
instability, which leads to norm inflation of size νκ$^{−\frac{1}{3}}$ .
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) |
| Publikationstyp | Zeitschriftenaufsatz |
| Publikationsdatum | 31.08.2025 |
| Sprache | Englisch |
| Identifikator | ISSN: 0951-7715, 1361-6544 KITopen-ID: 1000184444 |
| Erschienen in | Nonlinearity |
| Verlag | Institute of Physics Publishing Ltd (IOP Publishing Ltd) |
| Band | 38 |
| Heft | 8 |
| Seiten | Art.-Nr.: 085019 |
| Vorab online veröffentlicht am | 26.08.2025 |
| Nachgewiesen in | Scopus Web of Science OpenAlex Dimensions |