  We established the existence, uniqueness and stability of subsonic flows past
an airfoil with a vortex line at the trailing edge. Such a flow pattern is
governed by the two dimensional steady compressible Euler equations. The vortex
line attached to the trailing edge is a contact discontinuity for the Euler
system and is treated as a free boundary. The problem is formulated and solved
by using the implicit function theorem. The main difficulties are due to the
fitting of the vortex line with the profile at the trailing edge and the
possible subtle instability of the vortex line at the far field. Suitable
choices of the weights and elaborate barrier functions are found to deal with
such difficulties.
