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

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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