On the Irrotational Approximation to Adiabatic Chaplygin Gas Dynamic System

In this paper we mainly study the difference of the weak solutions generated by a wave front tracking algorithm for the steady adiabatic Chaplygin gas dynamic system and the steady irrotational system. Under the hypothesis that the initial data are of sufficiently small total variation, we prove that the difference between the solutions to these two systems can be bounded by the cube of the total variation of the initial perturbation.