Abstract: We show that the maxwellian density corresponding to a smooth solutions of the Euler equations for compressible flows of an ideal gas solves a transport-collapse-type equation. The transport part is the transport of the density in the space direction with a fixed transport velocity, and the collapse part corresponds to the transport in the velocity direction along a vector from the subdifferential of the indicator function of the set of maxwillians in the space of regular probability measures with the 2-Wasserstein metric.