  We derive a new kinetic and a porous medium equations from the nonlinear
Schr\"odinger equation with random potentials. The kinetic equation has a very
similar form with the 4-wave turbulence kinetic equation in the wave turbulence
theory. Moreover, we construct a class of self-similar solutions for the porous
medium equation. These solutions spread infinitely as time goes to infinity and
this fact answers the 'weak turbulence' question for the nonlinear
Schr\"odinger equation with random potentials positively. We also derive Ohm's
law for the porous medium equation.
