Stability of Transonic Shock-Fronts in Three-Dimensional Conical Steady Potential Flow past a Perturbed Cone

摘要

For an upstream supersonic flow past a straight-sided cone in $\R^3$ whosevertex angle is less than the critical angle, a transonic (supersonic-subsonic)shock-front attached to the cone vertex can be formed in the flow. In thispaper we analyze the stability of transonic shock-fronts in three-dimensionalsteady potential flow past a perturbed cone. We establish that the self-similartransonic shock-front solution is conditionally stable in structure withrespect to the conical perturbation of the cone boundary and the upstream flowin appropriate function spaces. In particular, it is proved that the slope ofthe shock-front tends asymptotically to the slope of the unperturbedself-similar shock-front downstream at infinity.