Existence of global bounded smooth solutions for the one‐dimensional nonisentropic Euler system

Abstract

We study the existence of global bounded smooth solutions to the one-dimensional (1D) nonisentropic Euler system with large initial data. We derive a group of characteristic decompositions for the 1D nonisentropic Euler system. Using these characteristic decompositions, we find some sufficient conditions on the initial data to obtain the existence of global bounded classical solutions to the Cauchy problem. By the method of characteristic decomposition, we also give a type of large initial data to show the formation of singularity for the 1D nonisentropic Euler system.