Some results on free boundary problems of incompressible ideal magnetohydrodynamics equations

Abstract

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⩾2) when the Taylor sign condition is satisfied and the free boundaries are closed.

Keywords

• free boundary problems
• incompressible ideal magnetohydrodynamics equations
• ill-posedness
• linearized problem
• well-posedness