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

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

2011-01-24

arxiv.org/abs/1101.4527v2

Mathematics

Analysis of PDEs

51 pages; v2: introduction reworked and references added

Scientific paper

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 $x\in\R\times\T^3$.

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