  We prove that the solutions of the defocusing cubic wave equation on T2 exist
globally in time in Hs(T2) for s > 2/5 by contradiction. Assuming that one of
the maximal times of existence is finite, we prove that the Sobolev norm of
each of these solutions is bounded in an open neighborhood of it by estimating
the growth of a mollified energy through the interpolation with the potential
bound for the low frequency part.
