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Hyperbolic nonlinear Schrödinger equations on $${\mathbb {R}}\times {\mathbb {T}}$$ R × T

Author

Listed:
  • Engin Başakoğlu

    (Institute of Mathematical Sciences, ShanghaiTech University)

  • Chenmin Sun

    (CNRS, Université Paris-Est Créteil, Laboratoire d’Analyse et de Mathématiques appliquées)

  • Nikolay Tzvetkov

    (Ecole Normale Supérieure de Lyon, UMPA, UMR CNRS-ENSL 5669)

  • Yuzhao Wang

    (School of Mathematics, University of Birmingham)

Abstract

In this paper, we consider the hyperbolic nonlinear Schrödinger equations (HNLS) on $${\mathbb {R}}\times {\mathbb {T}}$$ R × T . We obtain the sharp local well-posedness up to the critical regularity for cubic nonlinearity and in critical spaces for higher odd nonlinearities. Moreover, when the initial data is small, we prove the global existence and scattering for the solutions to HNLS with higher nonlinearities (except the cubic one) in critical Sobolev spaces. The main ingredient of the proof is the sharp up to the endpoint local/global-in-time Strichartz estimates.

Suggested Citation

  • Engin Başakoğlu & Chenmin Sun & Nikolay Tzvetkov & Yuzhao Wang, 2025. "Hyperbolic nonlinear Schrödinger equations on $${\mathbb {R}}\times {\mathbb {T}}$$ R × T," Partial Differential Equations and Applications, Springer, vol. 6(6), pages 1-28, December.
    • Handle: RePEc:spr:pardea:v:6:y:2025:i:6:d:10.1007_s42985-025-00359-6
    DOI: 10.1007/s42985-025-00359-6
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    1. Kouichi Taira, 2020. "Strichartz estimates for non‐degenerate Schrödinger equations," Mathematische Nachrichten, Wiley Blackwell, vol. 293(4), pages 774-793, April.
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