On singularities of the polytropic flow of a compressible gas

The talk discusses the singularities of multivalued solutions of the Cauchy problem for equations of polytropic compressible gas with the adiabatic index $\gamma = 3$. For such solutions explicit solutions in quadratures are found, and the singularities of their projections on the plane of Euler coordinates are classified. Since these singularities are in correspondence with the gradient catastrophe and the onset of shock waves points, by that we classify the gradient catastrophe and the onset of shock waves points.
Joint work with I.A.Bogaevsky.