  In the field of differential equations, particularly fluid dynamics, many
researchers have shown an interest in the behavior of time periodic solutions.
In this paper, we study isentropic gas flow in a bounded interval and apply a
time periodic outer force. This motion is described by the compressible Euler
equation with the outer force. Our purpose in this paper is to prove the
existence of a time periodic solutions. Unfortunately, little is known for the
system of conservation laws until now. The problem seems to lie in fact that
the equation does not possesses appropriate decay estimates.

Analysis of PDEs