Short-range scattering of Hartree type fractional NLS

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• 作者：Yonggeun Cho ^{changocho@jbnu.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35Q55 ; 35Q40
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 January 2017
• 年：2017
• 卷：262
• 期：1
• 页码：116-144
• 全文大小：374 K

文摘

In this paper we consider scattering problem for Hartree type fractional NLS with |∇|^α$|\mathrm{\nabla }{|}^{\alpha }$ (1<α<2$1<\alpha <2$) and potential V∼|x|^−γ$V\sim |x{|}^{-\gamma }$. We show small data scattering in a weighted space for the short range . The difficulty arises from the non-locality and non-smoothness of |∇|^α$|\mathrm{\nabla }{|}^{\alpha }$. To overcome it we utilize the method of commutator estimate based on Balakrishnan's formula.