Year: 2024
Type: preprint
Abstract: We consider the electron magnetohydrodynamics (MHD) equation on the 3D torus $\mathbb T^3$. For a given smooth vector field $H$ with zero mean and zero divergence, we can construct a weak solution $B$ to the electron MHD in the space $L^γ_tW^{1,p}_x$ for appropriate $(γ, p)$ such that $B$ is arbitrarily close to $H$ in this space. The parameters $γ$ and $p$ depend on the resistivity. As a consequence, non-uniqueness of weak solutions is obtained for the electron MHD with hyper-resistivity. In particular, non-Leray-Hopf solutions can be constructed. As a byproduct, we also show the existence of weak solutions to the electron MHD without resistivity.
Source: arXiv (Cornell University)
Author: Dai, Mimi
Institution: University of Illinois Chicago
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4398796207