Riemann problem for a particle-fluid coupling

We present a model of coupling between a point wise particle and a compressible inviscid fluid following the Euler equations. The interaction between the fluid and the particle is achieved through a drag force. It writes as the product of a discontinuous function and a Dirac measure. After defining the solution, we solve the Riemann problem with a fixed particle for arbitrary data. We exhibit a set of condition on the drag force under which there exists a unique self-similar solution.