GLOBAL NONISENTROPIC ROTATIONAL SUPERSONIC FLOWS IN A SEMI-INFINITE DIVERGENT DUCT

Supersonic flows for the two-dimensional (2D) steady full Euler system are studied. We construct a global nonisentropic rotational supersonic flow in a semi-infinite divergent duct. The flow satisfies the slip condition on the walls of the duct, and the state of the flow is given at the inlet of the duct. The solution is constructed by the method of characteristics. The main difficulty for the global existence is that a uniform a priori C 1 norm estimate of the solution is hard to obtain, especially when the solution tends to vacuum state. We derive a group of characteristic decompositions for the 2D steady full Euler system. Using these decompositions, we obtain uniform a priori estimates for the derivatives of the solution. A sufficient condition for the appearance of vacuum is also given. We show that if there is a vacuum then the vacuum is always adjacent to one of the walls, and the interface between gas and vacuum must be straight. The method used here also may be used to construct some other 2D steady nonisentropic rotational supersonic flows.