On the global existence and stability of a multi-dimensional supersonic conic shock wave (Q2249760)

In this paper, the authors consider three-dimensional steady potential equations which describe the motion of a supersonic polytropic gas past an infinitely long circular cone with a sharp angle. By establishing a global uniform weighted energy estimate, the authors show that a multi-dimensional conic shock attached to the vertex of the cone exists globally provided the Mach number of the incoming supersonic flow is sufficiently large. In this result, a key assumption of spherical symmetry on the perturbed supersonic which is needed in some known results is removed. Further, the authors study the asymptotic behavior of the three-dimensional supersonic conic shock solution.