Singularity formation for the 1D model of EMHD

In this paper, we study the singularity formation phenomenon of the 1D model of Electron Magnetohydrodynamics (EMHD). we will construct a solution whose $C^3$-norm blows up in finite time. In the end, we will show that the solution is in $C^{\mathrm{\infty }}(\mathbb{R}\mathrm{\backslash }\{0\})\cap C^{3,s}(\mathbb{R})\cap H^3(\mathbb{R})$ and is not asymptotically self-similar.