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

A rigorous mathematical analysis is given for a magnetohydrodynamic boundary layer problem, which arises in the study of self-similar solutions of the two-dimensional steady laminar boundary layer flow for an incompressible electrically conducting non-dilatable fluid (i.e., a Newtonian fluid or a pseudo-plastic one) along an isolated surface in the presence of an exterior magnetic field orthogonal to the flow. For this problem, only a normal solution has the physical meaning. The uniqueness, existence, and nonexistence results for normal solutions are established. Also the asymptotic behavior of the normal solution at the infinity is displayed. Received: January 10, 2007; revised: September 6, 2007, April 21, 2008