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

• Published in: Nonlinear analysis Vol. 205; p. 112261
• Main Authors: Cho, Yonggeun, Lee, Kiyeon
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-04-2021
• Subjects: Blowup; Focusing energy-critical nonlinearity; GWP; Inhomogeneous NLS; Kenig–Merle argument; Scattering; Weighted space; GWP; Focusing energy-critical nonlinearity; Scattering; 35Q55; Inhomogeneous NLS; Blowup; 35Q40; Weighted space; Kenig–Merle argument
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2021.112261

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 0≤b<43 by Kenig–Merle argument based on the standard Strichartz estimates. Here we extend the GWP to the coefficient with more serious singularity, 43≤b<32. For this purpose, we improve the local theory and develop a new profile decomposition based on weighted Strichartz estimates.