Spatially inhomogeneous solutions of the averaged chain of the equations of the kinetic theory of gases in the case of systems with a strong statistical coupling

The chain of equations averaged at time intervals of the order of free run time is deduced from the Bogolubov chain of equations in the first order in the Van der Waals number (a rarefyness parameter). This chain can be used for describing macroscopic processes without any assumptions about the relations between functions of different orders. In the case when the initial values of a finite number $q$ of the lower distribution functions are known, all the distribution functions can be expressed in terms of $q$ new functions, for which the chain takes the form of a closed system of equations. The methods of solution as well as some properties of the solutions are considered for the system obtained. In particular, the un-monotone character of the transition to the equilibrium is established for a considered class of physical systems and the turbulence problem is discussed.