Time-periodic solution to nonhomogeneous isentropic compressible Euler equations with time-periodic boundary conditions

TL;DR

This paper proves the existence and uniqueness of time-periodic supersonic solutions for one-dimensional nonhomogeneous isentropic compressible Euler equations with time-periodic boundary conditions, using energy methods.

Contribution

It introduces a new approach to establish the existence and uniqueness of time-periodic solutions under specific boundary conditions for these equations.

Findings

Existence of time-periodic supersonic solutions

Uniqueness of these solutions after a certain time

Application of energy methods to prove results

Abstract

In this paper, we study one-dimensional nonhomogeneous isentropic compressible Euler equations with time-periodic boundary conditions. With the aid of the energy methods, we prove the existence and uniqueness of the time-periodic supersonic solutions after some certain time.