Existence of global bounded smooth solutions for the one‐dimensional nonisentropic Euler system. (5th October 2020)

• Record Type: Journal Article
• Authors: Lai, Geng; Zhao, Qing
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 2(2021)
• Page Start: 2226
• Page End: 2236
• Publication Date: 2020-10-05
• Subjects: characteristic decompositions -- classical solution -- Compressible Euler equations -- vacuum; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6933
• Languages: English
• ISSNs: 0170-4214

Abstract

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.