Small data scattering of hartree type fractional schrödinger equations in a scaling critical space

Yonggeun Cho, Tohru Ozawa, Changhun Yang

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we study the small-data scattering of Hartree type fractional Schrödinger equations in space dimension 2, 3. It has Lévy index a between 1 and 2, and Hartree type nonlinearity F(u) = µ(|x|-y*|u|2)u with 2d/(2d - 1) < y < 2, y ≥ α > 1. This equation is scaling-critical in Hsc with sc (y-α)/2. We show that the solution scatters in Hsc,1 where Hsc, 1 is also a scaling critical space of Sobolev type taking in angular regularity with norm defined by. For this purpose we use the recently developed Strichartz estimate which is L2θ -averaged on the unit sphere Sd-1.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalFunkcialaj Ekvacioj
Volume64
Issue number1
DOIs
Publication statusPublished - 2021

Keywords

  • Angularly averaged strichartz estimate
  • Hartree type fractional schrödinger equation
  • Scaling critical space
  • Small data scattering

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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