Boundary value problems for the 2D steady relativistic Euler equations with general equation of state. (October 2018) - Chen, Jianjun; Lai, Geng; Zhang, Jiayi
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.