Decay and Scattering of Solutions to Nonlinear Schrödinger Equations with Regular Potentials for Nonlinearities of Sharp Growth
Year: 2017
Author: Ze Li, Lifeng Zhao
Journal of Mathematical Study, Vol. 50 (2017), Iss. 3 : pp. 277–290
Abstract
In this paper, we prove the decay and scattering in the energy space for nonlinear Schrödinger equations with regular potentials in $\mathbb{R}^d$ namely, $i∂_tu+Δu-V(x)u+ λ|u|^{p-1}u=0$. We will prove decay estimate and scattering of the solution in the small data case when $1+\frac{2}{d}<p ≤ 1+\frac{4}{d-2}, d ≥ 3$. The index $1+\frac{2}{d}$ is sharp for scattering concerning the result of Strauss [22]. This result generalizes the one-dimensional work of Cuccagna et al. [4] to all $d ≥ 3$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v50n3.17.05
Journal of Mathematical Study, Vol. 50 (2017), Iss. 3 : pp. 277–290
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Nonlinear Schrödinger equations potential decay scattering.
Author Details
Ze Li Email
Lifeng Zhao Email
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