Sharp Condition for Global Existence of Supercritical Nonlinear Schrödinger Equation with a Partial Confinement

被引：0
|
作者：
Cheng-lin Wang
Jian Zhang
机构：
[1] University of Electronic Science and Technology of China,
来源：
Acta Mathematicae Applicatae Sinica, English Series | 2023年 / 39卷
关键词：
nonlinear Schrödinger equation; Bose-Einstein condensate; cross-constrained variational problem; global existence; sharp condition; 35Q55; 35A15; 35B30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study the L2-supercritical nonlinear Schrödinger equation (NLS) with a partial confinement, which is the limit case of the cigar-shaped model in Bose-Einstein condensate (BEC). By constructing a cross constrained variational problem and establishing the invariant manifolds of the evolution flow, we show a sharp condition for global existence.
引用
收藏
页码：202 / 210
页数：8
相关论文
共 50 条
  • [21] Nonlinear perturbations of a periodic Schrödinger equation with supercritical growth
    Giovany M. Figueiredo
    Olimpio H. Miyagaki
    Sandra Im. Moreira
    Zeitschrift für angewandte Mathematik und Physik, 2015, 66 : 2379 - 2394
  • [22] Existence in the nonlinear Schrödinger equation with bounded magnetic field
    Ian Schindler
    Cyril Tintarev
    Nonlinear Differential Equations and Applications NoDEA, 2022, 29
  • [23] Global Existence and Long-Term Behavior of a Nonlinear Schrödinger-Type Equation
    K. N. Soltanov
    Ukrainian Mathematical Journal, 2015, 67 : 74 - 97
  • [24] Strong Confinement Limit for the Nonlinear Schrödinger Equation Constrained on a Curve
    Florian Méhats
    Nicolas Raymond
    Annales Henri Poincaré, 2017, 18 : 281 - 306
  • [25] Sharp Global Well-Posedness for the Cubic Nonlinear Schrödinger Equation with Third Order Dispersion
    Carvajal, X.
    Panthee, M.
    JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2024, 30 (02)
  • [26] Global Well-Posedness for the Derivative Nonlinear Schrödinger Equation with Periodic Boundary Condition
    Bahouri, Hajer
    Perelman, Galina
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2024,
  • [27] Instantons, Fluctuations, and Singularities in the Supercritical Stochastic Nonlinear Schrödinger Equation
    Bureković, Sumeja
    Schäfer, Tobias
    Grauer, Rainer
    Physical Review Letters, 2024, 133 (07)
  • [28] Initial condition dependence and wave function confinement in the Schrödinger–Newton equation
    Marion Silvestrini
    Leonardo G. Brunnet
    Marcelo Disconzi
    Carolina Brito
    General Relativity and Gravitation, 2015, 47
  • [29] On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation
    A. de Bouard
    A. Debussche
    Probability Theory and Related Fields, 2002, 123 : 76 - 96
  • [30] Existence of solutions to the nonlinear Schrödinger equation on locally finite graphs
    Zidong Qiu
    Yang Liu
    Archiv der Mathematik, 2023, 120 : 403 - 416
12345