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

doi:10.3969/j.issn.1000-5641.201911029

Abstract

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

CLC Number:

O175.29

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.

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