Global Conic Shock Wave for the Steady Supersonic Flow Past a Curved Cone

Abstract

In this paper, we establish the global existence of a steady symmetric conic shock wave when a supersonic incoming flow hits a symmetric cone for a steady potential flow. The speed of the incoming flow is close to the limit speed, and the generatrix of the cone is assumed to have an attack angle less than a critical value and to have a decay rate on its second order derivatives. Based on a background solution, which is introduced here for the first time, we apply the characteristic method to construct the global solution.