@article{ba16b3a1857648129d7c8ab8a1424145,
title = "On global existence of L2 solutions for 1D periodic NLS with quadratic nonlinearity",
abstract = "We study the 1D nonlinear Schr{\"o}dinger 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.",
author = "Kazumasa Fujiwara and Vladimir Georgiev",
note = "Funding Information: The authors are grateful to the referees for helpful comments. K.F. was supported by the JSPS Grants-in-Aid for JSPS Fellows (Grant No. 19J00334) and JSPS Early Career Scientists (Grant No. 20K14337). V.G. was supported, in part, by INDAM, GNAMPA–Gruppo Nazionale per l{\textquoteright}Analisi Matematica, la Probabilit{\`a} e le loro Applicazioni; the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences; and the Top Global University Project, Waseda University, and Project No. PRA 2018 49 of the University of Pisa. Publisher Copyright: {\textcopyright} 2021 Author(s).",
year = "2021",
month = sep,
day = "1",
doi = "10.1063/5.0033101",
language = "English",
volume = "62",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics Publising LLC",
number = "9",
}