A class of accelerated solutions of the two-dimensional ideal magnetohydrodynamic equations

A particular class of exact solutions of the two-dimensional time-dependent magnetohydrodynamic equations for an ideal isothermal plasma is presented. The associated flows have non-vanishing acceleration. A special form of th e mapping between Eulerian and Lagrangian coordinates is assumed and the ac celeration term has to have the form of a potential force. The class of pot entials compatible with these assumptions is derived and the constraints im posed by the vanishing resistivity then lead to a restriction of the admiss ible flow fields. Some explicit solutions are constructed and their propert ies are investigated.