Existence of solutions to a model for sparse, one-dimensional fluids

We prove the global existence of solutions to a model for a viscous, compressible, barotropic fluid initially occupying a general open subset of a finite, one-dimensional interval. The fluid equations are applied only on the support of the density, understood in the sense of distributions. This support must be tracked and accommodation must be made for the possibly infinite number of collisions of fluid packets occurring on a possibly dense set of collision times. Our approach avoids certain nonphysical properties of solutions which are constructed as limits of solutions in which artificial mass has been inserted.