Open AccessSome results on free boundary problems of incompressible ideal magnetohydrodynamics equations
Author(s) -
Chengchun Hao,
AUTHOR_ID,
Tao Luo,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022021
Subject(s) - mathematics , sign (mathematics) , ideal (ethics) , magnetohydrodynamics , boundary value problem , boundary (topology) , compressibility , mathematical physics , mathematical analysis , physics , law , mechanics , magnetic field , quantum mechanics , political science
We survey some recent results related to free boundary problems of incompressible ideal magnetohydrodynamics equations, and present the main ideas in the proofs of the ill-posedness in 2D when the Taylor sign condition is violated given [ 1 ] , and the well-posedness of a linearized problem given in [ 2 ] in general $ n $-dimensions ($ n \geqslant 2 $) when the Taylor sign condition is satisfied and the free boundaries are closed.