On global existence and blow-up for damped stochastic nonlinear Schrödinger equation

Jianbo Cui, Jialin Hong, Liying Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)

Abstract

In this paper, we consider the well-posedness of the weakly damped stochastic nonlinear Schrödinger(NLS) equation driven by multiplicative noise. First, we show the global existence of the unique solution for the damped stochastic NLS equation in critical case. Meanwhile, the exponential integrability of the solution is proved, which implies the continuous dependence on the initial data. Then, we analyze the effect of the damped term and noise on the blow-up phenomenon. By modifying the associated energy, momentum and variance identity, we deduce a sharp blow-up condition for damped stochastic NLS equation in supercritical case. Moreover, we show that when the damped effect is large enough, the damped effect can prevent the blow-up of the solution with high probability.

Original languageEnglish
Pages (from-to)6837-6854
Number of pages18
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume24
Issue number12
DOIs
Publication statusPublished - Dec 2019
Externally publishedYes

Keywords

  • Blow-up
  • Exponential integrability
  • Global existence
  • Multiplicative noise
  • Stochastic nonlinear Schrödinger equation

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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