[1]周 凡,黄 娟*,李玉林.一类在磁场中具有调和势的非线性Schrdinger方程解整体存在和爆破的门槛条件[J].四川师范大学学报(自然科学版),2020,43(04):458-462.[doi:10.3969/j.issn.1001-8395.2020.04.006]
 ZHOU Fan,HUANG Juan,LI Yulin.Sharp Threshold of Global Existence and Blowup for the Nonlinear Schrdinger Equations with Harmonic Potential in Magnetic Field[J].Journal of SichuanNormal University,2020,43(04):458-462.[doi:10.3969/j.issn.1001-8395.2020.04.006]
点击复制

一类在磁场中具有调和势的非线性Schrödinger方程解整体存在和爆破的门槛条件()
分享到:

《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
43卷
期数:
2020年04期
页码:
458-462
栏目:
基础理论
出版日期:
2020-06-20

文章信息/Info

Title:
Sharp Threshold of Global Existence and Blowup for the Nonlinear Schrödinger Equations with Harmonic Potential in Magnetic Field
文章编号:
1001-8395(2020)04-0458-05
作者:
周 凡12 黄 娟12* 李玉林12
1. 四川师范大学 数学科学学院, 四川 成都 610066; 2. 四川师范大学 可视化计算与虚拟现实四川省重点实验室, 四川 成都 610066
Author(s):
ZHOU Fan12 HUANG Juan12 LI Yulin12
1. School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066, Sichuan; 2. Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
磁场 调和势 整体存在 爆破 门槛条件
Keywords:
magnetic field harmonic potential global existence blowup sharp threshold condition
分类号:
O175.5
DOI:
10.3969/j.issn.1001-8395.2020.04.006
文献标志码:
A
摘要:
研究在磁场中一类带调和势的非线性Schrödinger方程.通过分析方程的性质,结合Gagliardo-Nirenberg不等式,得出在正能量情况下其解整体存在和爆破的门槛条件.
Abstract:
In this paper, we discuss the nonlinear Schrödinger equations with harmonic potential in magnetic field. By analyzing the properties of the equations and combining the Gagliardo-Nirenberg inequality, we obtain the sharp threshold of global existence and blowup for the equations in positive energy case.

参考文献/References:

[1] CAZENAVE T, ESTEBAN M J. On the stability of stationary states for nonlinear Schrödinger equations with an external magnetic field[J]. Comput Appl Math,1988,7(3):155-168.
[2] CINGOLANI S. Semiclassical stationary states of nonlinear Schrödinger equations with an external magnetic field[J]. J Diff Eqns,2003,188(1):52-79.
[3] TINTAREV K. Nonlinear subelliptic Schrödinger equations with external magnetic field[J]. Electron J Diff Eqns,2004,136(2):281-286.
[4] BONHEURE D, CINGOLANI S, NYS M. Nonlinear Schrödinger equation:concentration on circles driven by an external magnetic field[J]. Calc Var Part Diff Eqns,2016,55(4):1-33.
[5] GAN Z H, GUO B L. Blow-up phenomena of the vector nonlinear Schrödinger equations with magnetic fields[J]. Sci China:Math,2011,54(10):2111-2122.
[6] GAN Z H, ZHANG J. Blow-up, global existence and standing waves for the magnetic nonlinear Schrödinger equations[J]. Discrete Contin Dyn Syst,2013,A32(3):827-846.
[7] GINIBRE J, VELO G. Scattering theory for the Schrödinger equation in some external time dependent magnetic fields[J]. J Diff Eqns,2005,215(1):108-177.
[8] 舒级,成和平. 一类带外部磁场的非线性Schrödinger方程解的爆破和整体存在[J]. 四川师范大学学报(自然科学版),2006,29(5):512-515.
[9] RIBEIRO G. Finite time blow-up for some nonlinear Schrödinger equations with an external magnetic field[J]. Nonlinear Anal:TMA,1991,16(11):941-948.
[10] RIBEIRO G. Instability of symmetric stationary states for some nonlinear Schrödinger equations with an external magnetic field[J]. Ann Inst H Poincare:Phys Theory,1991,54(4):403-433.
[11] LAURENT M. Remarks on non-linear Schrödinger equation with magnetic fields[J]. Commun Part Diff Eqns,2008,33(7):1198-1215.
[12] NAKAMURA Y. Local solvability and smoothing effects of nonlinear Schrödinger equations with magnetic fields[J]. Funkc Ekvacioj,2001,44(1):1-18.
[13] BOUARD A. Nonlinear Schrödinger equations with magnetic fields[J]. Diff Integral Eqns,1991,4:73-88.
[14] GALATI L, ZHENG S. Nonlinear Schrödinger equations for Bose-Einstein condensates[J]. Am Inst Phys,2013,1562(1):50-64.
[15] LIU W, WANG C. Infinitely many solutions for the nonlinear Schrödinger equations with magnetic potentials in RN[J]. J Math Phys,2013,54(12):121508.
[16] GARCIA A. Magnetic virial identities and applications to blow-up for Schrödinger and wave equations[J]. J Phys Math Theory,2012,45(1):015202.
[17] CINGOLANI S. Semiclassical stationary states of nonlinear Schrödinger equations with an external magnetic field[J]. J Diff Eqns,2003,188(1):52-79.
[18] WEINSTEIN M I. Nonlinear Schrödinger equations and sharp interpolation estimates[J]. Commun Math Phys,1983,87(4):567-576.
[19] GLASSEY R T. On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations[J]. J Math Phys,1977,18(9):1794-1797.

相似文献/References:

[1]李姣,张健*.具临界非线性项的随机非线性Schrödinger方程的整体解[J].四川师范大学学报(自然科学版),2010,(02):143.
 LI Jiao,ZHANG Jian.Global Solution for the Stochastic Nonlinear Schrödinger Equation with Critical Nonlinear Term[J].Journal of SichuanNormal University,2010,(04):143.
[2]舒级,张健.吸引玻色爱因斯坦凝聚的坍塌性质[J].四川师范大学学报(自然科学版),2004,(04):331.
 SHU Ji~(),ZHANG Jian~ (. College of Mathematics and Software Science,Sichuan Normal University,et al.[J].Journal of SichuanNormal University,2004,(04):331.
[3]刘刚,蒲志林.一类带调和势的非线性Schrdinger方程在R~2中整体解存在的充分条件[J].四川师范大学学报(自然科学版),2005,(05):529.
 LIU Gang~(),PU Zhi-lin~(. Editor Office of Journal of Sichuan Normal University(Natural Science),Sichuan Normal University,et al.[J].Journal of SichuanNormal University,2005,(04):529.
[4]王颖,甘在会,林群.一类带调和势Schrdinger方程组解的爆破[J].四川师范大学学报(自然科学版),2004,(01):18.
 WANG Ying,GAN Zai-hui,LIN Qun(College of Mathematics and Software Science,et al.[J].Journal of SichuanNormal University,2004,(04):18.
[5]林群,甘在会,王颖.一类带调和势的非线性阻尼Schrdinger方程[J].四川师范大学学报(自然科学版),2004,(01):22.
 LIN Qun,GAN Zai-hui,WANG Ying(College of Mathematics and Software Science,et al.[J].Journal of SichuanNormal University,2004,(04):22.
[6]舒级,张健.低维空间中吸引玻色—爱因斯坦凝聚的坍塌性质[J].四川师范大学学报(自然科学版),2004,(03):230.
 SHU Ji,ZHANG Jian (College of Mathematics and Software Science,Sichuan Normal University,et al.[J].Journal of SichuanNormal University,2004,(04):230.
[7]舒级,张健.一类带阻尼项的Gross-Pitaevskii方程在二维空间中的坍塌性质[J].四川师范大学学报(自然科学版),2003,(02):120.
 SHU Ji,ZHANG Jian(College of Mathematics and Software Science,Sichuan Normal University,et al.[J].Journal of SichuanNormal University,2003,(04):120.
[8]刘妍丽,张健.一类带调和势的非线性Schrdinger方程的整体解[J].四川师范大学学报(自然科学版),2002,(02):142.
 LIU Yan li,ZHANG Jian (College of Mathematics and Software Science,Sichuan Normal University,et al.[J].Journal of SichuanNormal University,2002,(04):142.
[9]张健,舒级.低维空间中带调和势的非线性Schrdinger方程[J].四川师范大学学报(自然科学版),2002,(03):226.
 ZHANG Jian,SHU Ji (College of Mathematics and Software Science,Sichuan Normal University,et al.[J].Journal of SichuanNormal University,2002,(04):226.
[10]周展宏.带调和势的非线性Schrdinger方程爆破解的爆破率[J].四川师范大学学报(自然科学版),2007,(06):0.
 ZHOU Zhan-hong(Faculty of Science,Guangdong Ocean University,Zhanjiang 088,et al.[J].Journal of SichuanNormal University,2007,(04):0.

备注/Memo

备注/Memo:
收稿日期:2018-06-10 接受日期:2018-11-13
基金项目:国家自然科学基金(11401409)和四川省科技计划项目(2018JY0486)
*通信作者简介:黄 娟(1981—),女,教授,主要从事偏微分方程和数学物理的研究,E-mail:hjmath@qq.com
更新日期/Last Update: 2020-06-20