Global conic shock wave for the steady supersonic flow past a cone: Isothermal case

We establish the global existence and stability of a steady symmetric conic shock wave for the perturbed supersonic isothermal flow past an infinitely long circular cone with an arbitrary vertex angle. The flow is assumed to be described by a steady potential equation. By establishing the uniform weighted energy estimate on the linearized problem, we show that the symmetric 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.