CONSTRUCTION OF TWO-BUBBLE SOLUTIONS FOR THE ENERGY-CRITICAL NLS

被引：18
|
作者：
Jendrej, Jacek [1 ]
机构：
[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA
来源：
ANALYSIS & PDE | 2017年 / 10卷 / 08期
关键词：
nonlinear Schrodinger equation; energy-critical; multisoliton; NONLINEAR SCHRODINGER-EQUATION; GLOBAL WELL-POSEDNESS; BLOW-UP; GROUND-STATE; DYNAMICS; SCATTERING; COMPACTNESS;
D O I：
10.2140/apde.2017.10.1923
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We construct pure two-bubbles for the energy-critical focusing nonlinear Schrodinger equation in space dimension N >= 7. The constructed solution is global in (at least) one time direction and approaches a superposition of two stationary states both centered at the origin, with the ratio of their length scales converging to 0. One of the bubbles develops at scale 1, whereas the length scale of the other converges to 0 at rate vertical bar t vertical bar-2/N-6. The phases of the two bubbles form the right angle.
引用
收藏
页码：1923 / 1959
页数：37
相关论文
共 50 条
  • [41] Limiting coarsening of a two-bubble foam with viscosity
    Schneider, Maxime
    Wailliez, Julian
    Alves, Douglas
    Gay, Cyprien
    Rio, Emmanuelle
    In, Martin
    Salonen, Anniina
    COLLOIDS AND SURFACES A-PHYSICOCHEMICAL AND ENGINEERING ASPECTS, 2024, 688
  • [42] Two-bubble interaction under the sound field
    Zhang Peng-Li
    Lin Shu-Yu
    ACTA PHYSICA SINICA, 2009, 58 (11) : 7797 - 7801
  • [43] Two-bubble instabilities in quasi-two-dimensional foams
    Vaz, MF
    Cox, SJ
    PHILOSOPHICAL MAGAZINE LETTERS, 2005, 85 (08) : 415 - 425
  • [44] SCATTERING FOR THE TWO-DIMENSIONAL ENERGY-CRITICAL WAVE EQUATION
    Ibrahim, Slim
    Majdoub, Mohamed
    Masmoudi, Nader
    Nakanishi, Kenji
    DUKE MATHEMATICAL JOURNAL, 2009, 150 (02) : 287 - 329
  • [45] The derivation of the T3 energy-critical NLS from quantum many-body dynamics
    Chen, Xuwen
    Holmer, Justin
    INVENTIONES MATHEMATICAE, 2019, 217 (02) : 433 - 547
  • [46] Decay Estimates for Nonradiative Solutions of the Energy-Critical Focusing Wave Equation
    Duyckaerts, Thomas
    Kenig, Carlos
    Merle, Frank
    JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (07) : 7036 - 7074
  • [47] GLOBAL WELL-POSEDNESS AND SCATTERING FOR DEFOCUSING ENERGY-CRITICAL NLS IN THE EXTERIOR OF BALLS WITH RADIAL DATA
    Li, Dong
    Smith, Hart
    Zhang, Xiaoyi
    MATHEMATICAL RESEARCH LETTERS, 2012, 19 (01) : 213 - 232
  • [48] Vortex shedding behind a rising bubble and two-bubble coalescence: A numerical approach
    Smolianski, A
    Haario, H
    Luukka, P
    APPLIED MATHEMATICAL MODELLING, 2005, 29 (07) : 615 - 632
  • [49] Decay Estimates for Nonradiative Solutions of the Energy-Critical Focusing Wave Equation
    Thomas Duyckaerts
    Carlos Kenig
    Frank Merle
    The Journal of Geometric Analysis, 2021, 31 : 7036 - 7074
  • [50] Dynamics of radial threshold solutions for generalized energy-critical Hartree equation
    Li, Xuemei
    Liu, Chenxi
    Tang, Xingdong
    Xu, Guixiang
    FORUM MATHEMATICUM, 2025,
12345