Hydromagnetic stability of gravitational streaming coaxial cylinders with double perturbed interfaces

The magnetohydrodynamic stability of streaming self-gravitational coaxial fluid cylinders with doubly perturbed interfaces has been developed. The problem is formulated and solved. A crucial feature of this work is that we have considered all mathematical solutions of the differential equations because singular solutions are not present at all in this case. Using appropriate boundary conditions, the stability criterion is derived and discussed analytically and numerically for determining the stable and unstable domains and their characteristics. 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.