Vacuum appearance in convex duct for van der Waals fluid

The present study concerns the motion of the supersonic flow, modeled by 2-D steady isentropic relativistic Euler system for van der Waals fluid inside a convex duct. We have used the hodograph transformation to analyze the interaction as well as a reflection of the characteristics in the (u, v)-plane. The existence of global solutions to the Goursat problems in inner and border regions have been discussed. The criterion for the vacuum appearance adjacent to the wall, involving the van der Waals parameters, has been established.