The logarithmic Schrödinger equation with spatial white noise on the full space

被引:0
|
作者
Chauleur, Quentin [1 ,2 ]
Mouzard, Antoine [3 ,4 ]
机构
[1] Univ Lille, INRIA Lille, F-59655 Villeneuve Dascq, France
[2] CNRS, UMR 8524 Lille, Lab Paul Painleve, Cite Sci, F-59655 Villeneuve Dascq, France
[3] ENS Paris, CNRS, 45 Rue Ulm, F-75005 Paris, France
[4] ENS Paris, Dept Math & Applicat, 45 Rue Ulm, F-75005 Paris, France
关键词
Logarithmic Schr & ouml; dinger equation; Multiplicative white noise; Global well-posedness; SCHRODINGER-EQUATION;
D O I
10.1007/s00028-024-01031-z
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We solve the Schr & ouml;dinger equation with logarithmic nonlinearity and multiplicative spatial white noise on Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}<^>d$$\end{document} with d <= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d\le 2$$\end{document}. Because of the nonlinearity, the regularity structures and the paracontrolled calculus can not be used. To solve the equation, we rely on an exponential transform that has proved useful in the context of other singular SPDEs.
引用
收藏
页数:28
相关论文
共 50 条
  • [21] New results concerning a Schrödinger equation involving logarithmic nonlinearity
    Cai, Yaqing
    Zhao, Yulin
    Luo, Chaoliang
    ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2024, (74) : 1 - 16
  • [22] Logarithmic transformation for the resonant nonlinear Schrödinger’s equation with parabolic nonlinearity equation
    K. El-Rashidy
    Aly R. Seadawy
    Optical and Quantum Electronics, 2022, 54
  • [23] Stochastic soliton and rogue wave solutions of the nonlinear Schrödinger equation with white Gaussian noise
    Wang, Wenzhuo
    Shi, Ying
    Zhao, Junxiao
    PHYSICS LETTERS A, 2024, 526
  • [24] The Time Fractional Schrödinger Equation on Hilbert Space
    Przemysław Górka
    Humberto Prado
    Juan Trujillo
    Integral Equations and Operator Theory, 2017, 87 : 1 - 14
  • [25] Asymptotic approximations for the phase space Schrödinger equation
    Karageorge, Panos D.
    Makrakis, George N.
    arXiv, 2021,
  • [26] The nonlinear Schrödinger equation in the half-space
    Antonio J. Fernández
    Tobias Weth
    Mathematische Annalen, 2022, 383 : 361 - 397
  • [27] On the theory of the Schrödinger equation with the full set of relativistic corrections
    Eremko, A.A.
    Brizhik, L.S.
    Loktev, V.M.
    Fizika Nizkikh Temperatur, 2018, 44 (06): : 734 - 746
  • [28] Existence and Multiplicity of Solutions for the Logarithmic Schrödinger Equation with a Potential on Lattice Graphs
    He, Zhentao
    Ji, Chao
    JOURNAL OF GEOMETRIC ANALYSIS, 2024, 34 (12)
  • [29] Spatial frequency range analysis for the nonlinear Schrödinger equation
    L. Z. Guo
    Y. Z. Guo
    S. A. Billings
    D. Coca
    Z. Q. Lang
    Nonlinear Dynamics, 2014, 78 : 93 - 102
  • [30] Time and Space Fractional Schrdinger Equation with Fractional Factor
    相培
    郭永新
    傅景礼
    CommunicationsinTheoreticalPhysics, 2019, 71 (01) : 16 - 26