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

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 $0\le b<\frac{4}{3}$. Here we extend the inhomogeneous index $b$ up to $\frac{3}{2}$. For this purpose, we improve the local theory and develop a new profile decomposition based on weighted space.

inhomogeneous NLS, weighted space, focusing energy-critical nonlinearity, GWP, scattering, blowup, Kenig-Merle argument. arXiv admin note: text overlap with arXiv:1905.10063

References in corpus (3)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities
• The Cauchy problem for the energy-critical inhomogeneous nonlinear Schrödinger equation

Cited by in corpus (1)

• Well-posedness and global dynamics for the critical Hardy-Sobolev parabolic equation