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arXiv · 2002.12355

On the focusing energy-critical inhomogeneous NLS: weighted space approach

Yongguen Cho·Kiyeon Lee
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Abstract

This paper is concerned with the global well-posedness and finite time blowup problem for the 3D focusing energy-critical inhomogeneous NLS. In the previous results \cite{chkl2, chkl3} the authors considered the same problems with the spatial inhomogeneity coefficient $g$ such that $g(x) \sim |x|^{-b}$ for $0 \le b < \frac43$. Here we extend the inhomogeneous index $b$ up to $\frac32$. For this purpose, we improve the local theory and develop a new profile decomposition based on weighted space.

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Yongguen Cho, Kiyeon Lee. 2020-02-27. On the focusing energy-critical inhomogeneous NLS: weighted space approach. https://doi.org/10.1016/j.na.2021.112261

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