On the stability of certain collisional configurations of hydromagnetic flows

We study the flow of a hydromagnetic fluid toward an obstacle in two different cases: when this is a rigid wall or when two plasma masses collide with each other. The magnetic field far from the obstacle is assumed to be aligned with the flow. The diffusivity is taken as low, and a boundary layer approach for the stationary MHD system is considered. The relevant equations turn out to be a generalization of the Falkner–Skan ones, and while analytical solutions are impossible to obtain, a qualitative analysis shows that whenever the size of the Alfvén speed far from the interface exceeds the size of the fluid velocity, the system has no nontrivial solutions. The interpretation of this is that in this case disturbances occurring in the boundary layer travel upstream and disturb the boundary conditions at the outer layers.