Scattering for the Quadratic Nonlinear Schrödinger System in <b><i>R</i></b>⁵ without Mass-Resonance Condition

• Hamano Masaru

  Saitama University

• Inui Takahisa

  Osaka University

• Nishimura Kuranosuke

  Tokyo University of Science

Abstract

We consider the quadratic nonlinear Schrödinger system (NLS system) on R⁵. The scattering below the ground state for NLS system was obtained by the first author under the mass-resonance condition. In this paper, we prove scattering below the ground state without the mass-resonance condition under the radially symmetric assumption. Our proof is based on the concentration compactness and the rigidity by Kenig-Merle (2006). Moreover, we discuss the concentration compactness and the rigidity for non-radial solutions.

Journal

• Funkcialaj Ekvacioj

  Funkcialaj Ekvacioj 64 (3), 261-291, 2021-12-15

  Division of Functional Equations, The Mathematical Society of Japan

Keywords

• Mass-resonance
• Virial identity
• Radial symmetry
• Scattering
• Quadratic Schrödinger system

Details

• CRID: 1390290473084145536
• NII Article ID: 130008131798
• DOI: 10.1619/fesi.64.261
• ISSN: 05328721
• Web Site: https://www.jstage.jst.go.jp/article/fesi/64/3/64_261/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed