Existence of solutions to a model for sparse, one-dimensional fluids
A model for a viscous, compressible, barotropic fluid initially occupying a general open subset of a finite, one-dimensional interval is considered. The author introduce a notation of weak solution which insures that the momentum of a fluid packet isolated from the spatial boundary on some time interval is conserved on that time interval. Then by tracking the fluid set and accommodate the possibly infinite number of collisions of fluid packets occurring on a possibly dense set of collision times, the author constructed a globally-locally momentum-conserving weak solution. The author's arguments can avoid some nonphysical properties of solutions resulting from the insertion of artificial mass.
scientific article; zbMATH DE number 5838460
scientific article