Communications in Mathematical Sciences

Volume 21 (2023)

Number 5

Global existence and stability of time-periodic solution to isentropic compressible Euler equations with source term

Pages: 1333 – 1348

DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n5.a7

Authors

Huimin Yu (School of Mathematics and Statistics, Shandong Normal University, Jinan, China)

Xiaomin Zhang (School of Mathematics and Statistics, Shandong Normal University, Jinan, China)

Jiawei Sun (School of Mathematics and Statistics, Shandong Normal University, Jinan, China)

Abstract

In this paper, we study the initial-boundary value problem of one-dimensional isentropic compressible Euler equations with the source term $\beta \rho {\lvert u \rvert}^\alpha u$. By means of wave decomposition and the uniform a priori estimates, we prove the global existence of smooth solutions under small perturbations around the supersonic Fanno flow. Then, by Gronwall’s inequality, we get that the smooth solution is time-periodic.

Keywords

isentropic compressible Euler equations, global existence, time-periodic solutions, supersonic Fanno flow, wave decomposition

2010 Mathematics Subject Classification

35A01, 35B10, 35Q31

Full Text (PDF format)

Received 3 January 2022

Received revised 12 September 2022

Accepted 13 October 2022

Published 30 August 2023