Skip to content
DraconiticResearch
Search Sources API
184,937 studies31 sourcesUpdated 13 min ago
PreprintarXiv licencearXiv

Schrödinger estimates with arbitrarily small periodic regularity on ℍ2 × 𝕋

  • Xuyi Wei
Open at sourcePDFDOICite

Abstract

Let M=ℍ2×𝕋 carry its product metric. We prove that the Schrödinger evolution maps L2(ℍ2;Hs(𝕋)) into L2([0,1];L6(M)) for every s>0, without any regularity assumption in the hyperbolic variable. The proof separates hyperbolic and periodic frequencies. A localized hyperbolic kernel estimate restricts the effective interaction time at hyperbolic frequency L to order L−1. Quadratic exponential sums then give a logarithmic bound when the periodic bandwidth is comparable to L. A mixed-norm decoupling argument, including an L6-valued extension and a periodic transference step, reduces wider periodic bands to this case. The infimum of the admissible periodic regularities is therefore zero. The estimate at zero regularity is not established here.

Related

  1. Polynomial Spectral Gap Estimates for Finitely Differentiable Quasi-Periodic Schrödinger Operators
    Ao Cai, Yang Gao, Jiawei He
    arXivPreprintarXiv licenceFull textAnalysis & PDEsDynamical systemsarXiv
  2. A sharp regularity threshold for Schrödinger maximal estimates on standard tori
    Xi Cen, Xitao Gao, Junyong Zhang
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  3. Two-scale estimates for limit-periodic Schrödinger operators
    Moises Gomez Solis
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsMathematical physicsarXiv
  4. Work in progress: A Lean-verified conditional reduction of periodic Navier-Stokes regularity on T^3 to a single integrability hypothesis
    Benjamin Frohman
    Zenodo (CERN European Organization for Nuclear Research)PreprintLicence not stated7 citedGeneral mathematicsOpenAlex
  5. Lp-regularity for fourth-order Schrödinger operators with unbounded or degenerate coefficients
    Federica Gregorio, Chiara Spina, Cristian Tacelli
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{wei2026schrödinger,
  title = {{Schrödinger estimates with arbitrarily small periodic regularity on $\mathbbH^2 \times \mathbbT$}},
  author = {Xuyi Wei},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27920},
  eprint = {2610.27920},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27920},
}
RIS
TY  - UNPB
TI  - Schrödinger estimates with arbitrarily small periodic regularity on ℍ^2 × 𝕋
AU  - Xuyi Wei
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27920
UR  - https://arxiv.org/abs/2610.27920
AB  - Let M=ℍ^2×𝕋 carry its product metric. We prove that the Schrödinger evolution maps L^2(ℍ^2;H^s(𝕋)) into L^2([0,1];L^6(M)) for every s>0, without any regularity assumption in the hyperbolic variable. The proof separates hyperbolic and periodic frequencies. A localized hyperbolic kernel estimate restricts the effective interaction time at hyperbolic frequency L to order L^−1. Quadratic exponential sums then give a logarithmic bound when the periodic bandwidth is comparable to L. A mixed-norm decoupling argument, including an L^6-valued extension and a periodic transference step, reduces wider periodic bands to this case. The infimum of the admissible periodic regularities is therefore zero. The estimate at zero regularity is not established here.
ER  -