Delta shock waves as limits of vanishing viscosity for 2-D steady pressureless isentropic flow

摘要

The Riemann problem for the two-dimensional steady pressureless isentropic flow in gas dynamics is solved completely. The Riemann solutions contain two kinds: delta-shock solutions and vacuum solutions. Under suitable generalized Rankine-Hugoniot relation and entropy condition, the existence and uniqueness of delta-shock solutions is established. Moreover, the stability of delta-shock solution to a reasonable viscous perturbation is proven. The numerical results coinciding with the theoretical solutions are also presented.