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

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 $g(x)\sim \mathrm{\mid }x{\mathrm{\mid }}^{-b}$ for $0 \le b < \frac43$\mathrm{.}Hereweextendtheinhomogeneousindex$b$upto$\frac32$. For this purpose, we improve the local theory and develop a new profile decomposition based on weighted space.