Abstract
An overview of some recent progress on magnetohydrodynamic stability and current sheet formation in a line-tied system is given. Key results on the linear stability of the ideal internal kink mode and resistive tearing mode are summarized. For nonlinear problems, a counterexample to the recent demonstration of current sheet formation by Low and Janse [Astrophys. J. 696, 821 (2009)] is presented, and the governing equations for quasistatic evolution of a boundary driven, line-tied magnetic field are derived. Some open questions and possible strategies to resolve them are discussed.
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