Steady self-similar inviscid flow

We consider solutions of the 2-d compressible Euler equations that are steady and self-similar. They arise naturally at interaction points in genuinely multi-dimensional flow. We characterize the possible solutions in the class of flows L^\infty-close to a constant supersonic background. As a special case we prove that solutions of 1-d Riemann problems are unique in the class of small L^\infty functions. We also show that solutions of the backward-in-time Riemann problem are necessarily BV.