Almost Morawetz estimates and global well-posedness for the defocusing $L^2$-critical nonlinear Schr{ö}dinger equation in higher dimensions

Details Almost Morawetz estimates and global well-posedness for the defocusing $L^2$-critical nonlinear Schr{ö}dinger equation in higher dimensions Almost Morawetz estimates and global well-posedness for the defocusing $L^2$-critical nonlinear Schr{ö}dinger equation in higher dimensions

2009-09-23

arxiv.org/abs/0909.4332v1

Mathematics

Analysis of PDEs

39 pages

Scientific paper

In this paper, we consider the global well-posedness of the defocusing, $L^{2}$ - critical nonlinear Schr{\"o}dinger equation in dimensions $n \geq 3$. Using the I-method, we show the problem is globally well-posed in $n = 3$ when $s > {2/5}$, and when $n \geq 4$, for $s > \frac{n - 2}{n}$. We combine energy increments for the I-method, interaction Morawetz estimates, and almost Morawetz estimates to prove the result.

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