  We are concerned with the global existence of entropy solutions for the
compressible Euler equations describing the gas flow in a nozzle with general
cross-sectional area, for both isentropic and isothermal fluids. New
viscosities are delicately designed to obtain the uniform bound of approximate
solutions. The vanishing viscosity method and compensated compactness framework
are used to prove the convergence of approximate solutions. Moreover, the
entropy solutions for both cases are uniformly bounded independent of time. No
smallness condition is assumed on initial data. The techniques developed here
can be applied to compressible Euler equations with general source terms.
