## Duke Mathematical Journal

### The energy-critical defocusing NLS on ${\mathbb{T}}^{3}$

#### Abstract

We prove global well-posedness in $H^{1}({\mathbb{T}}^{3})$ for the energy-critical defocusing initial-value problem $\begin{eqnarray*}(i\partial_{t}+\Delta)u=u|u|^{4},\quad u(0)=\phi.\end{eqnarray*}$

#### Article information

Source
Duke Math. J. Volume 161, Number 8 (2012), 1581-1612.

Dates
First available in Project Euclid: 22 May 2012

https://projecteuclid.org/euclid.dmj/1337690408

Digital Object Identifier
doi:10.1215/00127094-1593335

Mathematical Reviews number (MathSciNet)
MR2931275

Zentralblatt MATH identifier
1245.35119

#### Citation

Ionescu, Alexandru D.; Pausader, Benoit. The energy-critical defocusing NLS on ${\mathbb{T}}^{3}$. Duke Math. J. 161 (2012), no. 8, 1581--1612. doi:10.1215/00127094-1593335. https://projecteuclid.org/euclid.dmj/1337690408

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