Nonlinear stability of a self-similar 3-dimensional gas flow

We show that the 3-dimensional supersonic gas flow past an infinite cone is nonlinear staple upon the perturbation of the obstacle. The perturbed flow exists globally in space and tends to the self-similar flow downstream. There is a thin layer of concentration of vorticities and entropy variation. Our analysis is based on an approximation scheme using local self-similar solutions as building blocks. This enables us to obtain global estimates of the nonlinear interactions of waves needed for the stability analysis.