Multi-D variational principle and pressureless gas dynamics

The generalization of variational principle to multi-D systems of conservation laws and its connection with the notion of generalized solution are proposed. For the model multi-D system of pressureless gas the specific modification of the principle is found. Such modification is rendered in more details for 2D and 3D cases. Obtained representation allows describing the singularities formation mechanisms for the generalized solutions of pressureless gas system.