THE METHOD OF BOLTZMANN COLLISION INTEGRAL EIGENFUNCTIONS IN THE KINETIC-THEORY OF LONG-WAVE FLUCTUATIONS

Linearized general equations of long-wave fluctuation kinetics are sol ved (utilizing eigenfunctions and eigenvalues of the linearized Boltzm ann collision integral) in the asymptotic region t much greater than t au(r), (tau(r) is the relaxation time). A general form for linearized equations of the fluctuation hydrodynamics is obtained. Effective init ial conditions for the fluctuation hydrodynamics equations are derived for the case where fluctuations of any order are absent at the initia l moment. The time asymptotics of the one-particle distribution functi on are found at the evolutionary stage of the fluctuations where the f luctuations of hydrodynamic quantities play an essential role. This is compared with results of the ''long hydrodynamic tails'' theory obtai ned earlier.