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

In this paper we consider the global well-posedness (GWP) and finite time blowup problem for the 3D focusing energy-critical inhomogeneous NLS with spatial inhomogeneity the coefficient g such that g(x)∼|x|^−b for 0≤b<2. The difficulty of this problem comes from the singularity of g. In the previous result (Cho and Lee, 2020; Cho et al., 2020) the authors showed the GWP for [Figure presented] by Kenig–Merle argument based on the standard Strichartz estimates. Here we extend the GWP to the coefficient with more serious singularity, [Figure presented]. For this purpose, we improve the local theory and develop a new profile decomposition based on weighted Strichartz estimates.