Boundary value problems for the 2D steady relativistic Euler equations with general equation of state

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]+2p′(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.