Global Well-Posedness of the Energy-Critical Defocusing NLS on mathbbR ×mathbbT3{mathbb{R} times mathbb{T}^3}

摘要

We prove global well-posedness in H 1 for the energy-critical defocusing initial-value problem (i¶_t+D_x)u=u|u|2,    u(0)=f,{(ipartial_t+Delta_x)u=u|u|^2,quad u(0)=phi,} in the semiperiodic setting x Î mathbbR ×mathbbT3{xinmathbb{R} times mathbb{T}^3} .