  The recent observation of gravitational waves, stimulates the question of the
longtime evolution of the space-time fluctuations. Gravitational waves interact
themselves through the nonlinear character of Einstein's equations of general
relativity. This nonlinear wave interaction allows the spectral energy transfer
from mode to mode. According to the wave turbulence theory, the weakly
nonlinear interaction of gravitational waves leads to the existence of an
irreversible kinetic regime that dominates the longtime evolution. The
resulting kinetic equation suggests the existence of an equilibrium wave
spectrum and the existence of a non-equilibrium Kolmogorov-Zakharov spectrum
for spatio-temporal fluctuations. Evidence of these solutions extracted in the
fluctuating signal of the recent observations will be discussed in the paper.
Probably, the present results would be pertinent in the new age of development
of gravitational astronomy, as well as, in new tests of General Relativity.
