Subsonic time-periodic solution to compressible Euler equations with damping in a bounded domain

TL;DR

This paper proves the existence and stability of a unique subsonic time-periodic smooth solution to the one-dimensional compressible Euler equations with damping under periodic boundary conditions, modeling flows through porous media.

Contribution

It establishes the existence, uniqueness, and stability of subsonic time-periodic solutions with higher regularity under periodic boundary conditions for the damped Euler equations.

Findings

Existence of a unique subsonic time-periodic solution.

Stability of the solution under small initial perturbations.

Higher regularity achieved with smoother boundary conditions.

Abstract

In this paper, we consider the one-dimensional isentropic compressible Euler equations with linear damping $\beta(t,x)\rho u$ in a bounded domain, which can be used to describe the process of compressible flows through a porous medium.~And the model is imposed a dissipative subsonic time-periodic boundary condition.~Our main results reveal that the time-periodic boundary can trigger a unique subsonic time-periodic smooth solution which is stable under small perturbations on initial data. Moreover, the time-periodic solution possesses higher regularity and stability provided a higher regular boundary condition.