Riemann problem for the zero-pressure flow in gas dynamics

The Riemann problem for zero-pressure flow in gas dynamics in one dimension and two dimensions is investigated. Through studying the generalized Rankine-Hugoniot conditions of delta-shock waves, the one-dimensional Riemann solution is proposed which exhibits four different structures when the initial density involves Dirac measure. For the two-dimensional case, the Riemann solution with two pieces of initial constant states separated at a smooth curve is obtained.