| 中国科学院 数学与系统科学研究院 |
| 调和分析及其应用研究中心 |
| Center for Harmonic Analysis and its Applications, AMSS, CAS |
In the present paper, we show the ill-posedness of the free boundary problem of the incompressible ideal magnetohydrodynamics (MHD) equations in two spatial dimensions for any positive vacuum permeability $\mu_0$, in Sobolev spaces. The analysis is uniform for？any $\mu_0>0$.