The equations of motion of a collisionless continuum

The equations of motion of a collisionless continuum are derived within an Eulerian approach. They differ from the classical equations of motion of an ideal gas, which take into account heat conduction phenomena. Several problems related to the weak convergence of the solutions of the equations of motion of a continuum when there is an unbounded increase in time are discussed. The problem of the correctness of the operation of truncating the exact infinite chain of equations of a collisionless gas is examined.