非线性Schrödinger方程阈值解的Blow-up或Grow-up

IF 1.1 3区数学 Q2 MATHEMATICS, APPLIED

Dynamics of Partial Differential Equations Pub Date : 2022-09-11 DOI:10.4310/dpde.2023.v20.n3.a3

S. Gustafson, Takahisa Inui

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引用次数: 4

摘要

我们考虑了具有$L^{2}$-超临界和$H^{1}$-亚临界幂型非线性的非线性Schr\ {o}dinger方程。Duyckaerts和Roudenko以及Campos, Farah和Roudenko研究了与基态具有相同质量和能量的解的全局动力学。在这些论文中，假设有限方差来表示有限时间爆炸。在本文中，我们去掉了有限方差的假设，证明了一个膨胀或增长的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Blow-up or Grow-up for the threshold solutions to the nonlinear Schrödinger equation

We consider the nonlinear Schr\"{o}dinger equation with $L^{2}$-supercritical and $H^{1}$-subcritical power type nonlinearity. Duyckaerts and Roudenko and Campos, Farah, and Roudenko studied the global dynamics of the solutions with same mass and energy as that of the ground state. In these papers, finite variance is assumed to show the finite time blow-up. In the present paper, we remove the finite-variance assumption and prove a blow-up or grow-up result.

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来源期刊

Dynamics of Partial Differential Equations 数学-应用数学

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes novel results in the areas of partial differential equations and dynamical systems in general, with priority given to dynamical system theory or dynamical aspects of partial differential equations.