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

Engin Başakoğlu (), Chenmin Sun (), Nikolay Tzvetkov () and Yuzhao Wang ()
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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

Partial Differential Equations and Applications, 2025, vol. 6, issue 6, 1-28

Abstract: 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.

Keywords: Hyperbolic nonlinear Schrödinger equations; Critical Sobolev spaces; Local well-posedness; Global well-posedness; Primary 35A01; 35Q55 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42985-025-00359-6

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