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

Abstract

In this paper, we establish the global existence and stability of a steady symmetric shock wave for the constant supersonic flow past an infinitely long and large curved conic body. The flow is assumed to be polytropic, isentropic and described by a steady potential equation. Through looking for the suitable "dissipative" boundary conditions on the shock and the conic surface together with the special form of shock equation, we show that the conic shock attached at the vertex of the cone exists globally in the whole space when the speed of the supersonic incoming flow is appropriately large.