Two-dimensional jet flows for compressible full Euler system with general vorticity

TL;DR

This paper establishes the well-posedness and variational structure of two-dimensional subsonic jet flows for the steady full Euler system with general vorticity, including existence, uniqueness, and flow behavior analysis.

Contribution

It introduces a variational framework for analyzing 2D compressible jet flows with vorticity, extending previous methods to more general flow conditions.

Findings

Existence and uniqueness of smooth subsonic jet flows

Variational structure for the Euler system with vorticity

Characterization of far-field flow behavior and critical pressure

Abstract

In this paper, we consider the well-posedness theory of two-dimensional compressible subsonic jet flows for steady full Euler system with general vorticity. Inspired by the analysis in arXiv:2006.05672, we show that the stream function formulation for such system admits a variational structure. Then the existence and uniqueness of a smooth subsonic jet flow can be established by the variational method developed by Alt, Caffarelli and Friedman. Furthermore, the far fields behavior of the flow and the existence of a critical upstream pressure are also obtained.