On the existence of inviscid compressible steady flows through a three-dimensional bounded domain

Abstract

In this paper, we study the existence of steady flows of an inviscid compressible barotropic fluid through a bounded simply connected domain $\Omega \in \mathbb{R}^3$. We prove, under suitable conditions on the data, the existence and local uniqueness of a subsonic steady compressible flow satisfying a given mass flow per unit surface on the whole boundary of the domain, as well as two additional conditions on the inflow boundary.