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

On the interpolation with the potential bound for global solutions of the defocusing cubic wave equation on T2