Subsonic Euler flows in a three-dimensional finitely long cylinder with arbitrary cross section

Abstract

This paper concerns the well-posedness of subsonic flows in a three-dimensional finitely long cylinder with arbitrary cross section. We establish the existence and uniqueness of subsonic flows in the Sobolev space by prescribing the normal component of the momentum, the vorticity, the entropy, the Bernoulli's quantity at the entrance and the normal component of the momentum at the exit. One of the key points in the analysis is to utilize the deformation-curl decomposition for the steady Euler system introduced in \cite{WX19} to deal with the hyperbolic and elliptic modes. Another one is to employ the separation of variables to improve the regularity of solutions to a deformation-curl system near the intersection between the entrance and exit with the cylinder wall.