Chunjing Xie: Steady subsonic Euler flows through a nozzle or past a wall

We first discuss the well-posedness theory for subsonic
Euler flows in nozzles or past a symmetric body. One of the key
observations to achieve these results is that the streamlines in these
flows have simple topological structure. This helps us to introduce
the stream function formulation so that the compressible Euler system
can be reduced into a single second order equation. Finally, the
well-posedness theory for subsonic flows through nozzles with multiple
ends which share the key features for flows around a non-symmetric
body will be addressed. The key ingredients of the analysis are the
study for critical points of the solutions of elliptic equations and
the regularity of the solutions for elliptic equation around corners
with large inner angles.