Determining wavenumbers for Hall and electron magnetohydrodynamics turbulence

Hassan Babaei; Mimi Dai

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arXiv · 2604.10804

Determining wavenumbers for Hall and electron magnetohydrodynamics turbulence

Hassan Babaei·Mimi Dai

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Abstract

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.

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Hassan Babaei, Mimi Dai. 2026-04-12. Determining wavenumbers for Hall and electron magnetohydrodynamics turbulence. https://arxiv.org/abs/2604.10804

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