Large‐Time Existence and Decay of Entropy Solutions for Unsteady Isentropic Gas Flow in the Quasi‐One‐Dimensional Nozzle

ABSTRACT In this paper, we apply the viscosity–flux approximation method coupled with the maximum principle to obtain the a priori estimates for the viscosity approximation solutions of the unsteady isentropic gas flow in the de Laval nozzle. Then by applying the compensated compactness method, we obtain the global existence of entropy solutions. Finally, we study the large‐time behavior of solutions and show the decay of the norm of density for any adiabatic exponent .