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arXiv · 2312.13546

Subsonic time-periodic solution to damped compressible Euler equations with large entropy

Peng Qu·Huimin Yu·Xiaomin Zhang
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Abstract

In this paper, one-dimensional nonisentropic compressible Euler equations with linear damping $\alpha(x)\rho u$ 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.

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Peng Qu, Huimin Yu, Xiaomin Zhang. 2023-12-21. Subsonic time-periodic solution to damped compressible Euler equations with large entropy. https://arxiv.org/abs/2312.13546

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