Strong Instability of Standing Waves for the Nonlinear Schrodinger Equation in Trapped Dipolar Quantum Gases

被引：14

作者：

Feng, Binhua ^{[1
]}

Wang, Qingxuan ^{[2
]}

机构：

[1] Northwest Normal Univ, Dept Math, Lanzhou 730070, Peoples R China

[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2021年 / 33卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Dipolar quantum gases; Ground state standing waves; Strong instability; Partial; complete trapping potential; GROSS-PITAEVSKII EQUATION; SHARP THRESHOLD; HARTREE EQUATION; GLOBAL EXISTENCE; BLOWUP; STATES;

D O I：

10.1007/s10884-020-09881-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the strong instability of standing waves for the nonlinear Schrodinger equation arising in trapped dipolar quantum gases. Two cases are considered: the first when the system is free, the second when a partial/complete harmonic potential is added. In the free case, we present a new argument to prove that the ground state standing waves are strongly unstable by blow-up. In the second case, if partial derivative S-2(mu)omega(Q(omega)(mu))vertical bar(mu=1) <= 0, we deduce that the ground state standing wave u(t, x) = e(i omega t) Q(omega)(x) is strongly unstable by blow-up, where S-omega is the action, and Q(omega)(mu) = mu(3/2)Q(omega)(mu x) is the L-2-invariant scaling.

引用

页码：1989 / 2008

页数：20

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