Global well-posedness of the energy-critical defocusing NLS on $\mathbb{R}\times\mathbb{T}^3$

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Abstract

In this paper we prove global well-posedness in $H^1$ for the energy-critical defocusing initial-value problem \begin{equation*} (i\partial_t+\Delta_x)u=u|u|^2,\qquad u(0)=\phi, \end{equation*} in the semiperiodic setting $x\in\R\times\T^3$.