STRONG INSTABILITY OF STANDING WAVES FOR A SYSTEM NLS WITH QUADRATIC INTERACTION

doi:10.1007/s10473-020-0214-6

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (2): 515-528.doi: 10.1007/s10473-020-0214-6

STRONG INSTABILITY OF STANDING WAVES FOR A SYSTEM NLS WITH QUADRATIC INTERACTION

Van Duong DINH^1,2

1. Laboratoire Paul Painlevé UMR 8524, Université de Lille CNRS, 59655 Villeneuve d'Ascq, Cedex, France;
2. Department of Mathematics, HCMC University of Pedagogy, 280 An Duong Vuong, Ho Chi Minh, Vietnam

收稿日期:2018-12-28 出版日期:2020-04-25 发布日期:2020-05-26
作者简介:Van Duong DINH,E-mail:contact@duongdinh.com
基金资助:
The author is supported by the Labex CEMPI (ANR-11-LABX-0007-01).

STRONG INSTABILITY OF STANDING WAVES FOR A SYSTEM NLS WITH QUADRATIC INTERACTION

Van Duong DINH^1,2

1. Laboratoire Paul Painlevé UMR 8524, Université de Lille CNRS, 59655 Villeneuve d'Ascq, Cedex, France;
2. Department of Mathematics, HCMC University of Pedagogy, 280 An Duong Vuong, Ho Chi Minh, Vietnam

Received:2018-12-28 Online:2020-04-25 Published:2020-05-26
Supported by:
The author is supported by the Labex CEMPI (ANR-11-LABX-0007-01).

摘要/Abstract

摘要： We study the strong instability of standing waves for a system of nonlinear Schrödinger equations with quadratic interaction under the mass resonance condition in dimension d=5.

关键词: System NLS quadratic interaction, ground states, instability, blow-up

Abstract: We study the strong instability of standing waves for a system of nonlinear Schrödinger equations with quadratic interaction under the mass resonance condition in dimension d=5.

Key words: System NLS quadratic interaction, ground states, instability, blow-up

中图分类号:

35Q44

Van Duong DINH. STRONG INSTABILITY OF STANDING WAVES FOR A SYSTEM NLS WITH QUADRATIC INTERACTION[J]. 数学物理学报(英文版), 2020, 40(2): 515-528.

Van Duong DINH. STRONG INSTABILITY OF STANDING WAVES FOR A SYSTEM NLS WITH QUADRATIC INTERACTION[J]. Acta mathematica scientia,Series B, 2020, 40(2): 515-528.

[1] Cazenave T. Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics, 10. Courant Institute of Mathematical Sciences:American Mathematical Society, 2003
[2] Colin M, Colin T, Ohta M. Instability of standing waves for a system of nonlinear Schrödinger equations with three-wave interaction. Funkcial Ekvac, 2009, 52:371-380
[3] Colin M, Di Menza L, Saut J C. Solitons in quadratic media. Nonlinearity, 2016, 29:1000-1035
[4] Dinh V D. Existence, stability of standing waves and the characterization of finite time blow-up solutions for a system NLS with quadratic interaction. Nonlinear Anal, 2020, 190:111589
[5] Glassey R T. On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations. J Math Phys, 1977, 18:1794-1797
[6] Hamano M. Global dynamics below the ground state for the quadratic Schrödinger system in 5D. Preprint arXiv:1805.12245, 2018
[7] Hoshino G, Ozawa T. Analytic smoothing effect for a system of nonlinear Schrödinger equations. Differ Equ Appl, 2013, 5:395-408
[8] Hoshino G, Ozawa T. Analytic smoothing effect for a system of Schrödinger equations with two wave interaction. Adv Differential Equations, 2015, 20:697-716
[9] Hoshino G. Space-time analytic smoothing effect for global solutions to a system of nonlinear Schrödinger equations with large data. Ann Henri Poincaré, 2018, 19:2101-2114
[10] Hayashi N, Li C, Naumkin P I. On a system of nonlinear Schrödinger equation in 2D. Differential Integral Equations, 2011, 24:417-434
[11] Hayashi N, Li C, Naumkin P I. Modified wave operator for a system of nonlinear Schrödinger equations in 2D. Commun Partial Differential Equations, 2012, 37:947-968
[12] Hayashi N, Li C, Ozawa T. Small data scattering for a system of nonlinear Schrödinger equations. Differ Equ Appl, 2011, 3:415-426
[13] Hayashi N, Ozawa T, Tanaka K. On a system of nonlinear Schrödinger equations with quadratic interaction. Ann Inst H Poincaré Anal Non Linéaire, 2013, 30:661-690
[14] Ogawa T, Uriya K. Final state problem for a quadratic nonlinear Schrödinger system in two space dimensions with mass resonance. J Differential Equations, 2015, 258:483-583

[1]	陈化, 徐辉阳. GLOBAL EXISTENCE, EXPONENTIAL DECAY AND BLOW-UP IN FINITE TIME FOR A CLASS OF FINITELY DEGENERATE SEMILINEAR PARABOLIC EQUATIONS[J]. 数学物理学报(英文版), 2019, 39(5): 1290-1308.
[2]	王影, 王明新. BOUNDARY BLOW-UP RATE OF THE LARGE SOLUTION FOR AN ELLIPTIC COOPERATIVE SYSTEM[J]. 数学物理学报(英文版), 2019, 39(5): 1363-1379.
[3]	王亚, 梁玉霞. DISJOINT SUPERCYCLIC WEIGHTED PSEUDO-SHIFTS ON BANACH SEQUENCE SPACES[J]. 数学物理学报(英文版), 2019, 39(4): 1089-1102.
[4]	Jae-Myoung KIM. LOCAL EXISTENCE AND BLOW-UP CRITERION OF 3D IDEAL MAGNETOHYDRODYNAMICS EQUATIONS[J]. 数学物理学报(英文版), 2018, 38(6): 1759-1766.
[5]	Yue-Loong CHANG, Meng-Rong LI, C. Jack YUE, Yong-Shiuan LEE, Tsung-Jui CHIANG-LIN. MATHEMATICAL MODEL FOR THE ENTERPRISE COMPETITIVE ABILITY AND PERFORMANCE THROUGH A PARTICULAR EMDEN-FOWLER EQUATION u"-n^-q-1u (n)^q=0[J]. 数学物理学报(英文版), 2018, 38(4): 1311-1321.
[6]	林勇, 吴艺婷. BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS[J]. 数学物理学报(英文版), 2018, 38(3): 843-856.
[7]	朱新才. EXISTENCE AND BLOW-UP BEHAVIOR OF CONSTRAINED MINIMIZERS FOR SCHRÖDINGER-POISSON-SLATER SYSTEM[J]. 数学物理学报(英文版), 2018, 38(2): 733-744.
[8]	杨凌燕, 李晓光, 吴永洪, Louis CACCETTA. GLOBAL WELL-POSEDNESS AND BLOW-UP FOR THE HARTREE EQUATION[J]. 数学物理学报(英文版), 2017, 37(4): 941-948.
[9]	孔慧慧, 李海梁, 张兴伟. A BLOW-UP CRITERION OF SPHERICALLY SYMMETRIC STRONG SOLUTIONS TO 3D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY[J]. 数学物理学报(英文版), 2016, 36(4): 1153-1166.
[10]	朱圣国. BLOW-UP OF CLASSICAL SOLUTIONS TO THE COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH VACUUM[J]. 数学物理学报(英文版), 2016, 36(1): 220-232.
[11]	郑攀, 穆春来, 胡学刚, 张付臣. SECONDARY CRITICAL EXPONENT AND LIFE SPAN FOR A DOUBLY SINGULAR PARABOLIC EQUATION WITH A WEIGHTED SOURCE[J]. 数学物理学报(英文版), 2016, 36(1): 244-256.
[12]	段然, 江飞, 尹俊平. RAYLEIGH-TAYLOR INSTABILITY FOR COMPRESSIBLE ROTATING FLOWS[J]. 数学物理学报(英文版), 2015, 35(6): 1359-1385.
[13]	张裕隆, 李明融. A MATHEMATICAL MODEL OF ENTERPRISE COMPETITIVE ABILITY AND PERFORMANCE THROUGH EMDEN-FOWLER EQUATION FOR SOME ENTERPRISES[J]. 数学物理学报(英文版), 2015, 35(5): 1014-1022.
[14]	甘在会, 郭柏灵, 蒋芯. ORBITAL INSTABILITY OF STANDING WAVES FOR THE GENERALIZED 3D NONLOCAL NONLINEAR SCHRÖDINGER EQUATIONS[J]. 数学物理学报(英文版), 2015, 35(5): 1163-1188.
[15]	李玉环, 米永生, 穆春来. PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION[J]. 数学物理学报(英文版), 2014, 34(3): 748-758.

STRONG INSTABILITY OF STANDING WAVES FOR A SYSTEM NLS WITH QUADRATIC INTERACTION

STRONG INSTABILITY OF STANDING WAVES FOR A SYSTEM NLS WITH QUADRATIC INTERACTION

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0