Global three-dimensional subsonic Euler flows past an axisymmetric obstacle with large vorticity

TL;DR

This paper proves the existence and uniqueness of three-dimensional subsonic Euler flows around an axisymmetric obstacle with large vorticity, under broad conditions on upstream velocities and densities.

Contribution

It extends previous two-dimensional results to three dimensions, establishing existence, uniqueness, and asymptotic behavior of flows with large vorticity.

Findings

Existence and uniqueness of subsonic Euler flows past an obstacle.

Flow asymptotics derived from integral estimates.

Accommodation of flows with large vorticity under structural conditions.

Abstract

In this paper, we prove the existence and uniqueness of subsonic solutions to the steady Euler flows past a smooth, axisymmetric obstacle. Specifically, for a broad class of prescribed positive axial velocities in the upstream, the subsonic Euler flow exists provided that the upstream density exceeds a critical threshold. The non-degeneracy of the axial velocity is rigorously established by combining the strong maximum principle with a refined continuity argument. The asymptotic behavior of the flow is obtained from uniform integral estimates for the difference between the flow and the upstream state. In addition, this result accommodates flows with large vorticity under a structural condition, thereby differing from previous results in the two-dimensional case.