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 the mapping between Eulerian and Lagrangian coordinates is assumed and the acceleration term has to have the form of a potential force. The class of potentials compatible with these assumptions is derived and the constraints imposed by the vanishing resistivity then lead to a restriction of the admissible flow fields. Some explicit solutions are constructed and their properties are investigated.