L2 -decay rate for the critical nonlinear Schrödinger equation with a small smooth data

Takayoshi Ogawa, Takuya Sato

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We consider the Cauchy problem for the one dimensional nonlinear dissipative Schrödinger equation with a cubic nonlinearity λ| u| 2u, where λ∈ C with Im λ< 0. We show that a relation between L2-decay rate for the solution and a smoothness of the initial data. Our result improves the recent work of Hayashi–Li–Naumkin (Adv Math Phys Art. ID 3702738, 7, 2016) for the decay rate of L2.

Original languageEnglish
Article number18
JournalNonlinear Differential Equations and Applications
Volume27
Issue number2
DOIs
Publication statusPublished - 2020 Apr 1

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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