| 具临界非线性项的随机非线性Schrdinger方程的整体解 |
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| 引用本文： | 李姣,张健. 具临界非线性项的随机非线性Schrdinger方程的整体解[J]. 四川师范大学学报(自然科学版), 2010, 33(2). DOI: 10.3969/j.issn.1001-8395.2010.02.001 |
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| 作者姓名： | 李姣 张健 |
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| 作者单位： | 四川师范大学,数学与软件科学学院,四川,成都,610066 |
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| 摘 要： | 在二维空间中,讨论带调和势且具临界非线性项的一类随机非线性Schrdinger方程的Cauchy问题,在能量空间中研究其解整体存在的充分条件.借助于随机分析及偏微分方程的基本理论,利用It幃公式、鞅不等式和Gagliardo-Nirenberg不等式,通过估计能量泛函的期望得到在初值充分小时,Cauchy问题的解是整体存在的.
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| 关 键 词： | 非线性Schr(o)dinger方程 调和势 加性噪声 基态 整体解 |
Global Solution for the Stochastic Nonlinear Schr(o)dinger Equation with Critical Nonlinear Term |
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| LI Jiao,ZHANG Jian. Global Solution for the Stochastic Nonlinear Schr(o)dinger Equation with Critical Nonlinear Term[J]. Journal of Sichuan Normal University(Natural Science), 2010, 33(2). DOI: 10.3969/j.issn.1001-8395.2010.02.001 |
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| Authors: | LI Jiao ZHANG Jian |
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| Affiliation: | LI Jiao,ZHANG Jian(College of Mathematics , Software Software Science,Sichuan Normal University,Chengdu 610066,Sichuan) |
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| Abstract: | We discuss the Cauchy problem of the critical stochastic nonlinear Schr(o)dinger equation with a harmonic potential in two dimensional space.By using Itó formula,Martingale inequality,Gagliardo-Nirenberg inequality,and estimating the expectation of energy functional,we derive global existence of the solution for the equation with sufficiently small initial data. |
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| Keywords: | nonlinear Schr(o)dinger equation harmonic potential additive noise ground state global solution |
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