Journal of East China Normal University(Natural Science) >

2020 , Vol. 2020 >Issue 4: 64 - 71

DOI: https://doi.org/10.3969/j.issn.1000-5641.201911029

Mathematics

A new blow-up criterion for the nonhomogeneous nonlinear Schrödinger equation

  • LI Shuangshuang
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  • College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received date: 2019-06-26

  Online published: 2020-07-20

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Abstract

In this paper, the existence of blow-up solutions for the nonhomogeneous nonlinear Schrödinger equation is studied. First, a class of invariant sets is constructed and then the optimal Gagliardo-Nirenberg type inequality is applied; careful analysis is used to prove that for any large $\mu$, there exists $u_{0}\in H^{1}$ so that $E(u_{0})=\mu$ and the solution $u(t,x)$ with $u_{0}$ as an initial value blows up in finite time. This result supplements the existing content in the literature [1].

Key words： nonhomogeneous nonlinear Schrödinger equation; invariant set; blow-up

Cite this article

LI Shuangshuang . A new blow-up criterion for the nonhomogeneous nonlinear Schrödinger equation[J]. Journal of East China Normal University(Natural Science), 2020 , 2020(4) : 64 -71 . DOI: 10.3969/j.issn.1000-5641.201911029

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