Jx. Hu, THE RIEMANN PROBLEM FOR PRESSURELESS FLUID-DYNAMICS WITH DISTRIBUTIONSOLUTIONS IN COLOMBEAUS SENSE, Communications in Mathematical Physics, 194(1), 1998, pp. 191-205
The Riemann problem for the equations of pressureless fluid dynamics w
as considered. Solutions of this problem were constructed by employing
the viscosity vanishing approach. For some initial data, solutions sh
owed high singularity around the shock waves. A new mathematical theor
y of generalized functions initiated by J.F. Colombeau was applied to
dealing with the multiplication of singular distributions. As a byprod
uct, the entropy condition was obtained for singular distribution solu
tions.