  Our goal in this paper is to prove the global existence of a classical
solution for the isentropic nozzle flow. Regarding this problem, there exist
some global existence theorems of weak solutions. However, that of classical
solutions does not have much attention until now. When we consider the present
problem, the main difficulty is to obtain the uniform bound of solutions and
their derivatives. To solve this, we introduce an invariant region depending on
the space variable and a functional satisfying the Riccati equation along the
characteristic lines.
