On the solutions of the nonlinear Liouville hierarchy

We investigate the initial-value problem of the nonlinear Liouville hierarchy. For the general form of the interaction potential we construct a solution in terms of an expansion over particle clusters whose evolution is described by the corresponding-order cumulant of evolution operators of a system of finitely many particles. For the initial data from the space of integrable functions the existence of a strong solution of the Cauchy problem is proved