具有势的非线性Schrödinger方程的最小质量爆破解

IF 0.4 4区 数学 Q4 MATHEMATICS Tohoku Mathematical Journal Pub Date : 2020-07-31 DOI:10.2748/tmj.20211216
Naoki Matsui
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引用次数: 8

摘要

我们考虑以下非线性Schr{o}dinger势为$\mathbb{R}^N$的方程。我们研究了具有临界质量的初始值的存在性,对于该初始值,相应的解会爆炸。先前的一项研究证明了初始值的存在,当$N=1$或$2$时,相应的解决方案会爆炸。在这项工作中,在对维数$N$没有任何限制的情况下,我们构造了一个临界质量初始值,对应的解在有限时间内爆炸,并导出其爆炸率。
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Minimal mass blow-up solutions for nonlinear Schrödinger equations with a potential
We consider the following nonlinear Schr\"{o}dinger equation with a potential in $\mathbb{R}^N$. We studied the existence of an initial value with critical mass for which the corresponding solution blows up. A previous study demonstrated the existence of an initial value for which the corresponding solution blows up when $N=1$ or $2$. In this work, without any restrictions on the number of dimensions $N$, we construct a critical-mass initial value for which the corresponding solution blows up in finite time and derive its blow-up rate.
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来源期刊
CiteScore
0.80
自引率
0.00%
发文量
22
审稿时长
>12 weeks
期刊介绍: Information not localized
期刊最新文献
Analytic and Gevrey regularity for certain sums of two squares in two variables On the Blair's conjecture for contact metric three-manifolds Weighted $L^2$ harmonic 1-forms and the topology at infinity of complete noncompact weighted manifolds Erratum by editorial office: Minimal mass blow-up solutions for nonlinear Schrödinger equations with a potential (Tohoku Math.J. 75 (2023), 215--232) Invariant structure preserving functions and an Oka-Weil Kaplansky density type theorem
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