Characteristic decouplings and interactions of rarefaction waves of 2D Euler equations

This paper is concerned with classical solutions for the interaction of two arbitrary planar rarefaction waves for the self-similar Euler equations in two space dimensions. The approach is made up of various characteristic decompositions of the self-similar Euler equations for the speed of sound and inclination angles of characteristics, reported in an earlier paper [J. Li, Z. Yang, Y. Zheng, Characteristic decompositions and interactions of rarefaction waves of 2-D Euler equations, J. Differential Equations 250 (2011) 782–798]. Here we report a new decomposition of the characteristics that decouples the two derivatives of the speed of sound along the two families of characteristics, and we apply the decomposition to refine the global existence theory and convexity properties of the characteristics.