The Riemann problem with delta initial data for the two-dimensional steady zero-pressure adiabatic flow

Abstract

For the two-dimensional steady zero-pressure adiabatic flow, the Riemann problem with delta initial data is investigated and the global existence of generalized solution is established in four cases. Particularly, in solutions, a special type of nonclassical wave called the delta contact discontinuity with Dirac delta functions developing in both state variables is found. Furthermore, we show that the constructed generalized solutions are stable by the perturbation of initial data.