@Article{Han2012,
author = "Han, Pigong",
title = "Global well-posedness and scattering for the focusing nonlinear Schrödinger equation in the nonradial case",
journal = "Opuscula Math.",
year = "2012",
volume = "32",
number = "3",
pages = "487--504",
doi = "http://dx.doi.org/10.7494/OpMath.2012.32.3.487",
url = "http://dx.doi.org/10.7494/OpMath.2012.32.3.487",
abstract = "The energy-critical, focusing nonlinear Schrödinger equation in the nonradial case reads as follows: \[i\partial_t u = -\Delta u -|u|^{\frac{4}{N-2}}u,\quad (x,0)=u_0 \in H^1 (\mathbb{R}^N),\quad N\geq 3.\] Under a suitable assumption on the maximal strong solution, using a compactness argument and a virial identity, we establish the global well-posedness and scattering in the nonradial case, which gives a positive answer to one open problem proposed by Kenig and Merle [Invent. Math. 166 (2006), 645–675].",
keywords = "critical energy, focusing Schrödinger equation, global well-posedness, scattering",
issn = "1232-9274"
}