  We present our recent results on the Prandtl-Meyer reflection for supersonic
potential flow past a solid ramp. When a steady supersonic flow passes a solid
ramp, there are two possible configurations: the weak shock solution and the
strong shock solution. Elling-Liu's theorem (2008) indicates that the steady
supersonic weak shock solution can be regarded as a long-time asymptotics of an
unsteady flow for a class of physical parameters determined by certain
assumptions for potential flow. In this paper we discuss our recent progress in
removing these assumptions and establishing the stability theorem for steady
supersonic weak shock solutions as the long-time asymptotics of unsteady flows
for all the physical parameters for potential flow. We apply new mathematical
techniques developed in our recent work to obtain monotonicity properties and
uniform apriori estimates for weak solutions, which allow us to employ the
Leray-Schauder degree argument to complete the theory for the general case.
