Small data scattering of hartree type fractional schrödinger equations in dimension 2 and 3

Yonggeun Cho, Tohru Ozawa

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we study the small-data scattering of the d dimensional fractional Schrödinger equations with d = 2, 3, Lévy index 1 < α < 2 and Hartree type nonlinearity F (u) = µ(|x|−γ ∗ |u|2)u with max (Formula presented) < γ ≤ 2, γ < d. This equation is scaling-critical in Ḣsc, (Formula presented). We show that the solution scatters in Hs,1 for any s > sc, where Hs,1 is a space of Sobolev type taking in angular regularity with norm defined by (Formula presented). For this purpose we use the recently developed Strichartz estimate which is L2 -averaged on the unit sphere Sd−1 and utilize Up -Vp space argument.

Original languageEnglish
Pages (from-to)373-390
Number of pages18
JournalJournal of the Korean Mathematical Society
Volume55
Issue number2
DOIs
Publication statusPublished - 2018

Keywords

  • Angularly averaged Strichartz estimate
  • Hartree type fractional Schrödinger equation
  • Small data scattering
  • U and V spaces

ASJC Scopus subject areas

  • Mathematics(all)

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