The interaction of rarefaction waves of a two-dimensional nonlinear wave system

This paper is concerned with a two-dimensional Riemann problem for the nonlinear wave system which gives rise to an interaction of two planar rarefaction waves. This problem comes from the expansion of a wedge of gas with constant velocity into vacuum, which is often interpreted as the dam collapse problem in hydraulics. We establish the global existence of smooth solutions in the interaction region of rarefaction waves up to a non-trivial vacuum boundary.