Inertial flow of a continuous fluid generically has to develop singularities when and where trajectories of particles cross. Defining inertial motion of the fluid beyond singularities, motivated by application in Newtonian cosmology, thus becomes a nontrivial problem. Two topics will be discussed: (i) Bogaevski's recent result (math-ph/0407073) on transport within singular manifolds of inviscid Burgers flow and its extension to more general quasilinear equations of the Burgers/Hamilton-Jacobi type and (ii) variational formulations of zero-pressure gas dynamics in one and multiple dimensions.