Global entropy solutions to isentropic gas flows in general nozzles

In this paper, we prove the existence of global entropy solutions to the compressible Euler equations of isentropic gases in general nozzles provided that the geometric source term satisfies an integrability condition only without any upper bound restrictions. The crucial part of the proof is to construct uniformly bounded approximate solutions, which is achieved by adding viscosities to the [Formula: see text]-flux flows and establishing a new invariant region. The convergence of the approximate solutions is proved with the help of the compensated compactness framework.