Stability of Stationary Subsonic Compressible Euler Flows with Mass-Additions in Two-Dimensional Straight Ducts
Abstract
We show existence, uniqueness and stability for a family of stationary subsonic compressible Euler flows with mass-additions in two-dimensional rectilinear ducts, subjected to suitable time-independent multi-dimensional boundary conditions at the entrances and exits.The stationary subsonic Euler equations consist a quasi-linear system of elliptic-hyperbolic composite-mixed type, while addition-of-mass destructs the usual methods based upon conservation of mass and Lagrangian coordinates to separate the elliptical and hyperbolic modes of the system. We establish a new decomposition and nonlinear iteration scheme to overcome this major difficulty. It reveals that mass-additions introduce very strong interactions in the elliptic and hyperbolic modes, and lead to a class of second-order elliptic equations with multiple integral nonlocal terms. The linearized problem is solved by studying algebraicand analytical properties of infinite weakly coupled boundary-value problems of ordinary differential equations, each with multiple nonlocal terms, after applications of Fourier analysis methods.
Keywords
Cite
@article{arxiv.2202.03855,
title = {Stability of Stationary Subsonic Compressible Euler Flows with Mass-Additions in Two-Dimensional Straight Ducts},
author = {Junlei Gao and Hairong Yuan},
journal= {arXiv preprint arXiv:2202.03855},
year = {2022}
}