Year: 2023
Type: preprint
Abstract: In this paper, one-dimensional nonisentropic compressible Euler equations with linear damping $α(x)ρu$ are analyzed.~We want to explore the conditions under which a subsonic temporal periodic boundary can trigger a time-periodic $C^{1}$ solution. To achieve this aim, we use a technically constructed iteration scheme and give the sufficient conditions to guarantee the existence, uniqueness and stability of the $C^{1}$ time-periodic solutions on the perturbation of a subsonic Fanno flow.~It is worthy to be pointed out that the entropy exhibits large amplitude under the assumption that the inflow sound speed is small.~However, it is crucial to assume that the boundary conditions possess a kind of dissipative structure at least on one side, which is used to cancel the nonlinear accelerating effect in the system.~The results indicate that the time-periodic feedback boundary control with dissipation can stabilize the nonisentropic compressible Euler equations around the Fanno flows.
Source: arXiv (Cornell University)
Authors: Qu, Peng, Yu, Huimin, Zhang, Xiaomin
Institutions: Fudan University, Shandong Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4390136612