Concentration processes in the system of equations of gas dynamics without pressure

We consider a quasilinear system of equations of isentropic gas dynamics, where the pressure is formally set to zero. Such a system was considered by A.N. Kraiko in the late 70s at the physical level of severity. The model without pressure turns out to be useful for describing some complex physical phenomena, such as the evolution of multiphase flows, the movement of dispersed media, in particular drops or dust, the movement of granular media, etc. In addition, there is another interesting application of such a model in astrophysics, namely, a medium without pressure turns out to be a convenient tool for an approximate description of the large-scale distribution of matter in the Universe. Due to zero pressure, the system under consideration is not strictly hyperbolic and admits solutions in the form of measures on, generally speaking, manifolds of different dimensions. One-dimensional and two-dimensional cases will be considered. Theoretical results and numerical calculations will be presented, demonstrating the fundamental difference between one-dimensional and multidimensional cases.