Hydrodynamical behavior of Bose-Einstein condensate near the lambda point

Amplitude of the Bose-Einstein condensate wave function (ABCW), superfluid velocity and entropy density are chosen as a set of gross variables, and nonlinear kinetic equations for superfluid 4He near the lambda point are written explicitly. Relaxation time of ABCW near the lambda point is evaluated from contributions due to mode-mode couplings. A static correlation function of ABCW is assumed to be of the Ornstein-Zernike form. The relaxation time is shown to be independent of wave number in the long-wavelength limit and its value is estimated to be about xi/c2, where c2 and xi are the velocity of second sound and the critical correlation length, respectively. (auth.)