On Two-Dimensional Sonic-Subsonic Flow
Gui-Qiang Chen, Constantine Dafermos, Marshall Slemrod, and Dehua Wang
Abstract: A compensated compactness framework is established for sonic-subsonic approximate solutions to the two-imensional Euler equations for steady irrotational flows that may contain stagnation points. Only crude, readily available estimates are required for establishing compactness. It follows that the set of subsonic irrotational solutions to the Euler equations is compact; thus flows with sonic points over an obstacle, such as an airfoil, may be realized as limits of sequences of strictly subsonic flows. Furthermore, sonic-subsonic flows may be constructed from approximate solutions. The compactness framework is then extended to self-similar solutions of the Euler equations for unsteady irrotational flows.