Exact solutions of the aspherical axisymmetric gravo-magnetic condensation

We find exact and explicit solutions of the axisymmetric MHD equations of a self-gravitating polytropic gas. These solutions are able to describe a flat (uniform density) subsonic internal core, contracting homologously, of a collapsing cloud with aspherical pressure, aspherical gravitationnal potential, magnetic field and rotation. Two of the solutions describing the collapse of a rotating and magnetized cloud present outflow at the pole or at the equator.