Global Multidimensional Transonic Conic Shock Wave for the Perturbed Supersonic Flow Past a Cone

For the three-dimensional steady potential flow equation, in the reference [Z. Xin and H. Yin, Anal. Appl., (Singap.), 4 (2006), pp. 101–132], the authors have shown the global existence and stability of a multidimensional supersonic conic shock for the supersonic incoming flow past a sharp curved cone under the suitable boundary condition on the conic surface. In this paper, we will establish the global existence and stability of a multidimensional transonic conic shock wave for the steady perturbed supersonic flow past an infinitely long conic body when the pressure at infinity behind the conic shock surface is appropriately large.