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Global well-posedness and scattering for the three-dimensional defocusing cubic Schrödinger equation in Hs, s>1/2

  • Qingtang Su
  • Zehua Zhao
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Abstract

We prove global well-posedness and scattering for the three-dimensional defocusing cubic nonlinear Schrödinger equation with arbitrary initial data in Hs(R3), s>1/2, without radial symmetry. The proof combines the I-method with long-time L2t,x bounds for products of frequency-localized components of the nonlinear solution. The key high--low estimate follows from a directional interaction identity pairing high-frequency mass with low-frequency energy, together with an induction on frequency.

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Cite

BibTeXRIS
BibTeX
@misc{su2026global,
  title = {{Global well-posedness and scattering for the three-dimensional defocusing cubic Schrödinger equation in $H^s$, $s>\frac12$}},
  author = {Qingtang Su and Zehua Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.24830},
  eprint = {2609.24830},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24830},
}
RIS
TY  - UNPB
TI  - Global well-posedness and scattering for the three-dimensional defocusing cubic Schrödinger equation in H^s, s>1/2
AU  - Qingtang Su
AU  - Zehua Zhao
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.24830
UR  - https://arxiv.org/abs/2609.24830
AB  - We prove global well-posedness and scattering for the three-dimensional defocusing cubic nonlinear Schrödinger equation with arbitrary initial data in H^s(R^3), s>1/2, without radial symmetry. The proof combines the I-method with long-time L^2_t,x bounds for products of frequency-localized components of the nonlinear solution. The key high--low estimate follows from a directional interaction identity pairing high-frequency mass with low-frequency energy, together with an induction on frequency.
ER  -