Exact solution of the ideal magnetohydrodynamics equations, which describes a flow from the spherical source

Abstract:
We describe a plasma flow, which is governed by the partially invariant solution of the ideal magnetohydrodynamics equations. The solution was constructed on the group O(3) of rotations. We give a full picture of plasma flow, both stationary and nonstationary in 3D space. The solution describes a three-dimensional plasma flow from the spherical source. The flow takes place not in the whole space, but inside a disk-shaped domain. The solution has a functional arbitrariness, which allows us to vary the behavior of the plasma flow at the infinity.