Instability of Standing Waves for the Nonlinear Schrödinger–Poisson Equation in the L2-Critical Case
Instability of Standing Waves for the Nonlinear Schrödinger–Poisson Equation in the L2-Critical Case
复制标题
L2 临界情况下非线性薛定谔-泊松方程的驻波不稳定性
DOI：
10.1007/s10884-019-09779-6
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Qingxuan Wang
中科院分区：
文献类型：
--
作者：
Binhua Feng;Ruipeng Chen;Qingxuan Wang
In this paper, we consider the strong instability of standing waves for the nonlinear Schrödinger–Poisson equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} i\partial _t\psi +\Delta \psi -(|x|^{-1}*|\psi |^2)\psi +|\psi |^{p}\psi =0~~~~ (t,x)\in [0,T^*)\times {\mathbb {R}}^3. \end{aligned}$$\end{document}In the-critical case, i.e.,, we prove that the standing waves are strongly unstable by blow-up. This result is a complement to the result of Kikuchi (Adv Nonlinear Stud 7:403–437, ) and Bellazzini et al. (Proc Lond Math Soc 107:303–339, ), where the instability of standing waves were studied in the-supercritical case, i.e.,.
In this paper, we consider the strong instability of standing waves for the nonlinear Schrödinger–Poisson equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} i\partial _t\psi +\Delta \psi -(|x|^{-1}*|\psi |^2)\psi +|\psi |^{p}\psi =0~~~~ (t,x)\in [0,T^*)\times {\mathbb {R}}^3. \end{aligned}$$\end{document}In the-critical case, i.e.,, we prove that the standing waves are strongly unstable by blow-up. This result is a complement to the result of Kikuchi (Adv Nonlinear Stud 7:403–437, ) and Bellazzini et al. (Proc Lond Math Soc 107:303–339, ), where the instability of standing waves were studied in the-supercritical case, i.e.,.