Thursday, February 7, 2013

1302.1301 (Olga S Rozanova)

Exact solutions with singularities to ideal hydrodynamics of inelastic

Olga S Rozanova
We construct a large family of exact solutions to the hyperbolic system of 3 equations of ideal granular hydrodynamics in several dimensions for arbitrary adiabatic index $\gamma$. In dependence of initial conditions these solutions can keep smoothness for all times or develop singularity. In particular, in the 2D case the singularity can be formed either in a point or along a line. For $\gamma=-1$ the problem is reduced to the system of two equations, related to a special case of the Chaplygin gas. In the 1D case this system can be written in the Riemann invariant and can be treated in a standard way. The solution to the Riemann problem in this case demonstrate an unusual and complicated behavior.
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