On illposedness of the Hall and electron magnetohydrodynamic equations without resistivity on the whole space
| Autor: | Jeong, In-Jee, Oh, Sung-Jin |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | It has been shown in our previous work that the incompressible and irresistive Hall- and electron-magnetohydrodynamic (MHD) equations are illposed on flat domains $M = \mathbb{R}^k \times \mathbb{T}^{3-k}$ for $0 \le k \le 2$. The data and solutions therein were assumed to be independent of one coordinate, which not only significantly simplifies the systems but also allows for a large class of steady states. In this work, we remove the assumption of independence and conclude strong illposedness for compactly supported data in $\mathbb{R}^3$. This is achieved by constructing degenerating wave packets for linearized systems around time-dependent axisymmetric magnetic fields. A few main additional ingredients are: a more systematic application of the generalized energy estimate, use of the Bogovski\v{i} operator, and a priori estimates for axisymmetric solutions to the Hall- and electron-MHD systems. Comment: 36 pages |
| Databáze: | arXiv |
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