2D pressureless gas dynamics and variational principle

The paper considers the application of variational representation principle to the description of singularities formation for the generalized solutions of 2D gas dynamics without pressure. The basic difference from 1D situation is clarified. This difference reads as follows: in 2D case the argument of variational functional is a domain in 2D Euclidian space. The corresponding generalization of singularities’ emergency conditions is obtained.