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

2022/04/05 by Huimin Yu, Xiaomin Zhang, Yu, Huimin +3
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.2204.01939

Abstract

In this paper, we study the initial-boundary value problem of one-dimensional isentropic compressible Euler equations with the source term βρ|u|^αu. 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 the smooth solution is time-periodic.

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