Abstract:  In a sequence of papers Cathleen Morawetz formulated the idea of applying the method of compensated compactness (Luc Tartar, Francois Murat) to the analysis of two dimensional steady transonic compressible flow over an obstacle, e.g. an airfoil. In this talk I will summarize recent results of G-Q. Chen, M. Slemrod, D. Wang on an artificially viscous formulation of the transonic flow problem that allows us to proceed with Morawetz's program.