Characteristic Decompositions and Simple Waves of the 2D Steady Full Ultrarelativistic Euler Equations

ABSTRACT This paper studies the characteristic decomposition of the 2D steady full ultrarelativistic Euler equations, which is a nonstrictly reducible hyperbolic system. We obtain the characteristic decompositions by analyzing the characteristic form of the 2D steady full ultrarelativistic Euler equations and utilizing the commutator relation. Furthermore, we use the characteristic decompositions to prove the theory that “the ultrarelativistic flow in a region adjacent to a constant state is a simple wave”. Besides, simple wave solutions of this type are constructed.