On global existence of L2 solutions for 1D periodic NLS with quadratic nonlinearity

Kazumasa Fujiwara*, Vladimir Georgiev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study the 1D nonlinear Schrödinger equation with non-gauge invariant quadratic nonlinearity on the torus. The Cauchy problem admits trivial global dispersive solutions, which are constant with respect to space. The non-existence of global solutions has also been studied only by focusing on the behavior of the Fourier 0 mode of solutions. However, the earlier works are not sufficient to obtain the precise criteria for the global existence for the Cauchy problem. In this paper, the exact criteria for the global existence of L2 solutions are shown by studying the interaction between the Fourier 0 mode and oscillation of solutions. Namely, L2 solutions are shown a priori not to exist globally if they are different from the trivial ones.

Original languageEnglish
Article number091504
JournalJournal of Mathematical Physics
Issue number9
Publication statusPublished - 2021 Sep 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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