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PreprintarXiv licencearXiv

Unconditional uniqueness for the cubic nonlinear Schrödinger equation in H1/2(Bbb T3)

  • Yongming Luo
  • Jiayu Zheng
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Abstract

In this paper, we establish unconditional uniqueness for the cubic nonlinear Schrödinger equation (NLS) in the scaling-critical class H1/2(𝕋3). Unlike approaches based on the GP-hierarchy or normal form reductions, which typically involve higher-order expansions, our proof works directly with the original cubic NLS, where we also make use of several new a priori Euclidean-like Strichartz estimates. More precisely, we show that every distributional solution in CtHx1/2 belongs a priori to the class L2t,locLx6. The key ingredients are a suitable high-low modulation decomposition and the compactness of solution trajectories on bounded time intervals. We also exploit the preservation of the canonical symplectic form under the truncated NLS flow, in order to obtain necessary stability estimates in the rough Sobolev space H−1/2(𝕋3).

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Cite

BibTeXRIS
BibTeX
@misc{luo2026unconditional,
  title = {{Unconditional uniqueness for the cubic nonlinear Schrödinger equation in $H^1/2(\Bbb T^3)$}},
  author = {Yongming Luo and Jiayu Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34733},
  eprint = {2610.34733},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34733},
}
RIS
TY  - UNPB
TI  - Unconditional uniqueness for the cubic nonlinear Schrödinger equation in H^1/2(Bbb T^3)
AU  - Yongming Luo
AU  - Jiayu Zheng
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.34733
UR  - https://arxiv.org/abs/2610.34733
AB  - In this paper, we establish unconditional uniqueness for the cubic nonlinear Schrödinger equation (NLS) in the scaling-critical class H^1/2(𝕋^3). Unlike approaches based on the GP-hierarchy or normal form reductions, which typically involve higher-order expansions, our proof works directly with the original cubic NLS, where we also make use of several new a priori Euclidean-like Strichartz estimates. More precisely, we show that every distributional solution in C_tH_x^1/2 belongs a priori to the class L^2_t,locL_x^6. The key ingredients are a suitable high-low modulation decomposition and the compactness of solution trajectories on bounded time intervals. We also exploit the preservation of the canonical symplectic form under the truncated NLS flow, in order to obtain necessary stability estimates in the rough Sobolev space H^−1/2(𝕋^3).
ER  -