The leading-order hydrodynamics of the Landau-Vlasov kinectic equation with the nonlocal collision integral

This paper is devoted to the hydrodynamics of a one-component gas with small potential interaction. The basis of investigation is the kinetic equation in case of small potential interaction which contains general nonlocal collision integral and describes arbitrary non-uniform states. In the local approximation this equation coincides with the well-known Landau–Vlasov kinetic equation. In hydrodynamics the system is supposed to be weakly non-uniform.