Global Shock Waves¶for the Supersonic Flow Past a Perturbed Cone

We prove the global existence of a shock wave for the stationary supersonic gas flow past an infinite curved and symmetric cone. The flow is governed by the potential equation, as well as the boundary conditions on the shock and the surface of the body. It is shown that the solution to this problem exists globally in the whole space with a pointed shock attached at the tip of the cone and tends to a self-similar solution under some suitable conditions. Our analysis is based on a global uniform weighted energy estimate for the linearized problem. Combining this with the local existence result of Chen–Li 1] we establish the global existence and decay rate of the solution to the nonlinear problem. Received: 1 August 2001 / Accepted: 14 January 2002