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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 section 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.

Global Entropy Solutions to the Gas Flow in General Nozzle