The aim of this paper is to investigate the Cauchy problem for the periodic fifth order KP-I equation [partial_t u - partial_x^5 u -partial_x^{-1}partial_y^2u + upartial_x u = 0,~(t,x,y)inmathbb{R}timesmathbb{T}^2] We prove global well-posedness for constant $x$ mean value initial data in the space $mathbb{E} = {uin L^2,~partial_x^2 u in L^2,~partial_x^{-1}partial_y u in L^2}$ which is the natural energy space associated with this equation.
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