Year: 2025
Type: preprint
Abstract: We prove the non-uniqueness of weak solutions with non-trivial magnetic fields to the 3D Hall-MHD equations on the plane in the space $C^0_t L_x^2$ through the convex integration scheme and by constructing new errors and new intermittent flows. In particular, based on the construction of 3D intermittent flows, we obtain the $2\frac{1}{2}$D Mikado flows through a projection onto the plane. Moreover, we prove that the constructed weak solution do not conserve the magnetic helicity and find that weak solutions of the ideal Hall-MHD equations in $C^{\barβ}_{t,x}$ ($\barβ>0$) are the strong vanishing viscosity and resistive limit of weak solutions to the Hall-MHD equations.
Source: arXiv (Cornell University)
Authors: Peng, Yi, Wang, Huaqiao, Zhang, Chenlu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7075993849
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