Although we have dynamical theory, some characteristics of real fluids are missing. For example, the absence of heat flux implies that there is no transport of heat from one part to another. The tensor is diagonal, so there is no viscosity, which allows for the transport of momentum from one layer to another so that relative motions are damped out. In other words the Euler equations lack transport phenomena. We had assumed local Maxwellian distributions at all points without proof.
Transport phenomena occur when there are large gradients of temperature or velocity.
This is exactly the situation which required correction to the local Maxwellian distribution. To visualize the non-Maxwellian nature of the distribution necessary to cause transport phenomena consider a region where on one side the gas is hotter than on the other. Molecules from the hot gas with a distribution corresponding to the higher temperature will stream into the cold region and visa-versa. As a result of these molecular motions from different sides with different properties, the distribution function must have a departure from a pure Maxwellian. It is necessary to describe this departure to develop a theory of transport phenomena.