2018/11/19 by Guo, Qing, Wang, Hua, Yao, Xiaohua
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1811.07578
In this paper, we consider a 3d cubic focusing nonlinear Schrödinger equation (NLS) with slowing decaying potentials. Adopting the variational method of Ibrahim-Masmoudi-Nakanishi \citeIMN, we obtain a condition for scattering. It is actually sharp in some sense since the solution will blow up if it's false. The proof of blow-up part relies on the method of Du-Wu-Zhang \citeDWZ