GLOBAL EXISTENCE AND BLOW-UP FOR THE FOCUSING INHOMOGENEOUS NONLINEAR SCHRODINGER EQUATION WITH INVERSE-SQUARE POTENTIAL

被引：3
|
作者：
An, Jinmyong [1 ]
Jang, Roesong [1 ]
Kim, Jinmyong [1 ]
机构：
[1] Kim Il Sung Univ, Fac Math, Pyongyang, North Korea
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2023年 / 28卷 / 02期
关键词：
Inhomogeneous nonlinear Schrodinger equation; inverse-square potential; global existence; blow-up; ground state; ENERGY-CRITICAL NLS; SCATTERING;
D O I：
10.3934/dcdsb.2022111
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the Cauchy problem for the focusing inhomogeneous nonlinear Schrodinger equation with inverse-square potential iu(t) + Delta u - c|x|(-2)u + |x|(-b)|u|(sigma) u = 0; u(0) = u(0) is an element of H-c(1), (t, x) is an element of R x R-d, where d >= 3, 0 < b < 2, 4-2b/d < sigma < 4-2b/d-2 and c > -c(d) := -(d-2/2)(2). We first establish the criteria for global existence and blow-up of general (not necessarily radial or finite variance) solutions to the equation. Using these criteria, we study the global existence and blow-up of solutions to the equation with general data lying below, at, and above the ground state threshold. Our results extend the global existence and blow-up results of Campos-Guzman (Z. Angew. Math. Phys., 2021) and Dinh-Keraani (SIAM J. Math. Anal., 2021).
引用
收藏
页码：1046 / 1067
页数：22
相关论文
共 50 条
  • [1] Global existence, blow-up and mass concentration for the inhomogeneous nonlinear Schrodinger equation with inverse-square potential
    Jian, Hui
    Gong, Min
    Cai, Meixia
    ELECTRONIC RESEARCH ARCHIVE, 2023, 31 (12): : 7427 - 7451
  • [2] Global existence and blowup for a class of the focusing nonlinear Schrodinger equation with inverse-square potential
    Van Duong Dinh
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 468 (01) : 270 - 303
  • [3] Blow-up versus global well-posedness for the focusing INLS with inverse-square potential
    Deng, Mingming
    Lu, Jing
    Meng, Fanfei
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (03) : 3285 - 3293
  • [4] The nonlinear Schrodinger equation with an inverse-square potential
    Murphy, Jason
    NONLINEAR DISPERSIVE WAVES AND FLUIDS, 2019, 725 : 215 - 225
  • [5] ON GLOBAL EXISTENCE AND BLOW-UP FOR DAMPED STOCHASTIC NONLINEAR SCHRODINGER EQUATION
    Cui, Jianbo
    Hong, Jialin
    Sun, Liying
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (12): : 6837 - 6854
  • [6] Blow-up criteria for the inhomogeneous nonlinear Schrodinger equation
    Yang, Han
    Zhu, Shihui
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,
  • [7] Focusing nonlinear Hartree equation with inverse-square potential
    Chen, Yu
    Lu, Jing
    Meng, Fanfei
    MATHEMATISCHE NACHRICHTEN, 2020, 293 (12) : 2271 - 2298
  • [8] Scattering and Blow-Up Dichotomy of the Energy-Critical Nonlinear Schrödinger Equation With the Inverse-Square Potential
    Hamano, Masaru
    Ikeda, Masahiro
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2025,
  • [9] BLOW-UP FOR THE FOCUSING ENERGY CRITICAL NONLINEAR SCHRODINGER EQUATION WITH CONFINING HARMONIC POTENTIAL
    Cheng, Xing
    Gao, Yanfang
    COLLOQUIUM MATHEMATICUM, 2014, 134 (01) : 143 - 149
  • [10] Long time dynamics and blow-up for the focusing inhomogeneous nonlinear Schrodinger equation with spatially growing nonlinearity
    Dinh, Van Duong
    Majdoub, Mohamed
    Saanouni, Tarek
    JOURNAL OF MATHEMATICAL PHYSICS, 2023, 64 (08)
12345