Boundary value problems for the 2D steady relativistic Euler equations with general equation of state. (October 2018)

• Record Type: Journal Article
• Authors: Chen, Jianjun; Lai, Geng; Zhang, Jiayi
• Is Part Of: Nonlinear analysis. Volume 175(2018)
• Page Start: 56
• Page End: 72
• Publication Date: 2018-10
• Subjects: 35L65 -- 35L67; Relativistic Euler equations -- Goursat problem -- Mixed initial–boundary value problem -- Centered wave problem -- Relativistic jet -- Characteristic decomposition; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.05.007
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider several types of boundary value problems, including Goursat problem, mixed initial–boundary value problem, and centered wave problem for the two-dimensional steady relativistic Euler system with a general equation of state p = p ( ρ ) which is assumed to satisfy 0 < p ′ ( ρ ) < 1 and p ′ ′ ( ρ ) [ p ( ρ ) + ρ ] + 2 p ′ ( ρ ) [ 1 − p ′ ( ρ ) ] > 0 . Global classical solutions to these boundary value problems are constructed by the method of characteristic decomposition. Using these results, we also construct a global supersonic relativistic jet flow out of a semi-infinite convex duct intovacuum.