On a global supersonic-sonic patch characterized by 2-d steady full Euler equations (Q2196579)

The authors use the two-dimensional full Euler equations to study transonic patterns in a supersonic flow of a polytropic gas. The flow is not isentropic and the flow is not irrotational, at least behind the shock. New mathematical techniques are developed for solving the problem, including new characteristic decompositions and locally partial hodograph transformation using the Mach angle and the inclination angle of the streamline. The domain of the boundary-value problem is a curvilinear segment bounded by intersecting streamline curve and a characteristic curve. For superconic boundary data, global existence of a smooth solution is proved, and regularity of the solution is proved: the solution is \(C^{1,\frac16}\)-continuous up to the sonic curve and the sonic curve is also \(C^{1,\frac16}\)-continuous.