  The Cauchy problem for the system of equations of two-dimensional rotational
gas dynamics is considered. It is assumed that the Cauchy data are a smooth
compact perturbation of a constant state. Integral conditions for the data
sufficient for the loss of smoothness by a solution within a finite time are
found. We analyze the possibility of fulfilling these conditions and compare
them with the criterion of singularity formation, known for rotational gas
dynamics without pressure.
