On the global well-posedness of the quadratic NLS on H 1(T) + L 2(R)

Research output: Contribution to journal › Research article › Contributed › peer-review

Contributors

  • Leonid Chaichenets - , Institute of Analysis (Author)
  • Dirk Hundertmark - , Karlsruhe Institute of Technology (Author)
  • Peer Kunstmann - , Karlsruhe Institute of Technology (Author)
  • Nikolaos Pattakos - , Karlsruhe Institute of Technology (Author)

Abstract

We study the one dimensional nonlinear Schrödinger equation with power nonlinearity | u| α-1u for α∈ [1 , 5] and initial data u∈ H1(T) + L2(R). We show via Strichartz estimates that the Cauchy problem is locally well-posed. In the case of the quadratic nonlinearity (α= 2) we obtain global well-posedness in the space C(R, H1(T) + L2(R)) via Gronwall’s inequality.

Details

Original languageEnglish
Article number11
Number of pages28
JournalNoDEA Nonlinear Differential Equations and Applications
Volume28
Issue number2
Publication statusPublished - Mar 2021
Peer-reviewedYes

External IDs

Scopus 85100295178
Mendeley faf5d819-421d-3d05-8df1-fad943563dc0

Keywords

ASJC Scopus subject areas

Keywords

  • Schrödingergleichung, Wohlgestelltheit, Global well-posedness, Gronwall’s inequality, Local well-posedness, Nonlinear Schrödinger equation, Strichartz estimates