Large BV solution for isentropic gas dynamics system with initial data far from vacuum

Abstract We give the global existence results for the isentropic gas dynamics system with large BV initial data, assuming that the initial data are far from vacuum. The distance of the initial data from vacuum may be so large depending on the initial BV bounds. A new scaling framework is introduced , and we obtain the crucial BV bounds estimates of the vanishing viscosity solutions with the help of this framework coupled with the famous result for the corresponding small BV initial data given by Bianchini and Bressan.