bib for citation: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 $\mu_0>0$.
Comments: 28 pages Subjects: Analysis of PDEs (math.AP) Cite as: Commun. Math. Phys. 376, 259–286, 2020
@article{HL20,
author = {Hao, Chengchun and Luo, Tao},
title = {{Ill-Posedness of Free Boundary Problem of the Incompressible Ideal MHD}},
issn = {0010-3616},
doi = {10.1007/s00220-019-03614-1},
abstract = {{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 $\mu_0>0$.}},
pages = {259--286},
number = {1},
volume = {376},
journal = {Communications in Mathematical Physics},
year = {2020}
}