Global Existence of Smooth Solutions for the One-Dimensional Full Euler System for a Dusty Gas

doi:10.1007/s42967-022-00197-y

Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (3): 1235-1246.doi: 10.1007/s42967-022-00197-y

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Global Existence of Smooth Solutions for the One-Dimensional Full Euler System for a Dusty Gas

Geng Lai, Yingchun Shi

Department of Mathematics, Shanghai University, Shanghai, 200444, China

Received:2021-05-23 Revised:2021-05-23 Online:2023-09-20 Published:2023-08-29
Contact: Geng Lai,E-mail:laigeng@shu.edu.cn E-mail:laigeng@shu.edu.cn;shiyc@shu.edu.cn
Supported by:
This work is partially supported by the National Natural Science Foundation of China (12071278).

Abstract

Abstract: We study the existence of global-in-time classical solutions for the one-dimensional nonisentropic compressible Euler system for a dusty gas with large initial data. Using the characteristic decomposition method proposed by Li et al. (Commun Math Phys 267: 1–12, 2006), we derive a group of characteristic decompositions for the system. Using these characteristic decompositions, we find a sufficient condition on the initial data to ensure the existence of global-in-time classical solutions.

Key words: Compressible Euler system, Dusty gas, Classical solution, The method of characteristic decomposition

CLC Number:

Geng Lai, Yingchun Shi. Global Existence of Smooth Solutions for the One-Dimensional Full Euler System for a Dusty Gas[J]. Communications on Applied Mathematics and Computation, 2023, 5(3): 1235-1246.

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Global Existence of Smooth Solutions for the One-Dimensional Full Euler System for a Dusty Gas

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