Local Structural Stability of a Multidimensional Centered Rarefaction Wave for the Three-Dimensional Steady Supersonic Euler Flow around a Sharp Corner

As indicated in section 111 of Courant and Friedrichs's book [Supersonic Flow and Shock Waves, Interscience, New York, 1948], a supersonic flow around a sharp corner, one of the most important elementary flows, is effected by a rarefaction wave. This paper is concerned with the local structural stability problem on such a wave of a three-dimensional (3-D) steady full Euler system. More concretely, we establish the local existence and stability of a 3-D incomplete expansion centered rarefaction wave when the perturbed supersonic incoming flow moves around a sharp corner whose fixed wall beyond the corner is of a perturbation with respect to some oblique half-plane.