ИСТИНА

We construct a large family of exact solutions to the hyperbolic system of 3 equations of ideal granular hydrodynamics in several dimensions for arbitrary heat ratio. In dependence of initial conditions these solutions can keep smoothness for all times or develop singularity. In the latter case we show that the singularity in the component of density is integrable for spatial dimension greater than one. A special attention we pay to 2d case, where the singularity can be formed either in a point or along a line. We show that an initial vorticity prevents the formation of singularity. Further we consider a special case of the Chaplygin gas, where a special solution satisfies a couple of equations and therefore in 1D case the system can be written in the Riemann invariant and can be treated in a standard way (the criterion of the singularity formation can be found and the Riemann problem can be solved