Hydromagnetic stability of gravitational streaming coaxial cylinders with double perturbed interfaces

The magnetic fields interior and exterior to the fluid cylinders have stabilizing effects while the streaming is strongly destabilizing. The fluid densities ratio factor is stabilizing while that of the cylinders' radii ratio plays an important role in stabilizing the annular coaxial cylinders. The self-gravitational forces is destabilizing only for axisymmetric modes while it is stabilizing for the rest. Some reported and previously published works are obtained as limiting cases of the present general work.