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Scattering for the quadratic NLS system in ℝ5 without mass resonance or radial symmetry

  • Takahisa Inui
  • Kuranosuke Nishimura
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Abstract

We consider the quadratic NLS system i∂tu+Δu=vu̅,newline i∂tv+κΔv=u2, (t,x)∈ℝ×ℝ5, where κ>0. If κ=1/2, which is called mass resonance condition, then scattering below the ground state is shown by Hamano. Moreover, when κ≠ 1/2, scattering of radial solutions is proved in Hamano--Inui--Nishimura (2021). In the present paper, we prove scattering below the ground state for κ≠1/2 without radial symmetry. Our proof is based on the concentration compactness and rigidity method by Kenig--Merle (2006). For the rigidity argument, following Pausader (2010), we use a localized virial argument in the direction orthogonal to the momentum.

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Cite

BibTeXRIS
BibTeX
@misc{inui2026scattering,
  title = {{Scattering for the quadratic NLS system in $\mathbbR^5$ without mass resonance or radial symmetry}},
  author = {Takahisa Inui and Kuranosuke Nishimura},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32364},
  eprint = {2609.32364},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32364},
}
RIS
TY  - UNPB
TI  - Scattering for the quadratic NLS system in ℝ^5 without mass resonance or radial symmetry
AU  - Takahisa Inui
AU  - Kuranosuke Nishimura
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32364
UR  - https://arxiv.org/abs/2609.32364
AB  - We consider the quadratic NLS system i∂_tu+Δu=vu̅,newline i∂_tv+κΔv=u^2, (t,x)∈ℝ×ℝ^5, where κ>0. If κ=1/2, which is called mass resonance condition, then scattering below the ground state is shown by Hamano. Moreover, when κ≠ 1/2, scattering of radial solutions is proved in Hamano--Inui--Nishimura (2021). In the present paper, we prove scattering below the ground state for κ≠1/2 without radial symmetry. Our proof is based on the concentration compactness and rigidity method by Kenig--Merle (2006). For the rigidity argument, following Pausader (2010), we use a localized virial argument in the direction orthogonal to the momentum.
ER  -