Self-similar solutions of the magnetohydrodynamic boundary layer system for a dilatable fluid

Summary A rigorous mathematical analysis is given for a magnetohydrodynamic boundary layer problem, which arises in the two-dimensional steady laminar boundary layer flow for an incompressible electrically conducting dilatable fluid along an isolated surface in the presence of an exterior magnetic field orthogonal to the flow. In the self-similar case, the problem is transformed into a third-order nonlinear ordinary differential equation with certain boundary conditions, which is proved to be equivalent to a singular initial value problem for an integro-differential equation of first order. With the aid of the singular initial value problem, the uniqueness, existence, and nonexistence results for generalized normal solutions are established.