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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2604.10804 |
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| _version_ | 1866918441149005824 |
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| author | Babaei, Hassan Dai, Mimi |
| author_facet | Babaei, Hassan Dai, Mimi |
| contents | In turbulent flows, the Kolmogorov wavenumber characterizes the smallest scales at which viscous effects dominate. A mathematical analogue of this notion first introduced by Foias and Prodi [8] -- a determining wavenumber -- quantifies the minimal set of modes that uniquely determine the long-time behavior of solutions. Extending this framework from the Navier-Stokes equations to magnetized plasma models, we focus on the Hall-MHD and Electron-MHD turbulence in sub-ion and dissipation ranges.
We prove existence of time-dependent determining wavenumbers for weak solutions of the Hall- and electron-MHD, improving upon previous results that were not optimal and lacked any comparison with phenomenological dissipation scales. Under explicit scale-localized intermittency assumptions, we show that their time averages are bounded above by Kolmogorov-like dissipation wavenumbers predicted by phenomenological studies of plasma turbulence. For strong electron-MHD solutions, we also establish a uniform bound on the magnetic determining wavenumber from Besov regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10804 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Determining wavenumbers for Hall and electron magnetohydrodynamics turbulence Babaei, Hassan Dai, Mimi Analysis of PDEs In turbulent flows, the Kolmogorov wavenumber characterizes the smallest scales at which viscous effects dominate. A mathematical analogue of this notion first introduced by Foias and Prodi [8] -- a determining wavenumber -- quantifies the minimal set of modes that uniquely determine the long-time behavior of solutions. Extending this framework from the Navier-Stokes equations to magnetized plasma models, we focus on the Hall-MHD and Electron-MHD turbulence in sub-ion and dissipation ranges. We prove existence of time-dependent determining wavenumbers for weak solutions of the Hall- and electron-MHD, improving upon previous results that were not optimal and lacked any comparison with phenomenological dissipation scales. Under explicit scale-localized intermittency assumptions, we show that their time averages are bounded above by Kolmogorov-like dissipation wavenumbers predicted by phenomenological studies of plasma turbulence. For strong electron-MHD solutions, we also establish a uniform bound on the magnetic determining wavenumber from Besov regularity. |
| title | Determining wavenumbers for Hall and electron magnetohydrodynamics turbulence |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.10804 |