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

Geng Lai; Yingchun Shi

doi:10.1007/s42967-022-00197-y

Communications on Applied Mathematics and Computation ›› 2022, 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 ¹^,a
, Yingchun Shi ¹

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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.

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Geng Lai, Yingchun Shi. Global Existence of Smooth Solutions for the One-Dimensional Full Euler System for a Dusty Gas. Communications on Applied Mathematics and Computation, 2022, 5(3): 1235-1246 DOI:10.1007/s42967-022-00197-y