Abstract: We consider the singular Riemann problem for the isentropic compressible Euler equations, where the flux function is discontinuous due to the coexistence of a zero-pressure flow and a generalized Chaplygin gas. Under the over-compressing condition, we obtain a unique Radon measure-valued solution to the classical Riemann problem ($\rho_0=0$), and prove the existence of global solutions to the singular Riemann problem ($\rho_0>0$) for arbitrary initial data. For the case $\rho_0>0$, which generates a nonlinear delta shock, we analyze its interaction with other elementary waves. In particular, for solutions whose structure consists of a delta shock followed by a forward rarefaction wave $R_2$, we demonstrate that the delta shock inevitably interacts with $R_2$. This interaction manifests itself in the $(x,t)$-plane as the delta shock cutting through the rarefaction fan.

Key words: compressible Euler equations, Radon measure-valued solution, Riemann problem, Delta shock, discontinuous flux