Local Well-posedness of the Derivative Schrödinger Equation in Higher Dimension for Any Large Data

Boling GUO; Zhaohui HUO

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Local Well-posedness of the Derivative Schrödinger Equation in Higher Dimension for Any Large Data

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In this paper,the authors consider the local well-posedness for the derivative Schrödinger equation in higher dimension ut-iΔu+|u|^(2)(→γ·▽u)+u^(2)(→λ·▽-u)=0,(x,t)∈R^(n)×R,→γ,→λ∈R^(n);n≥2 It is shown that the Cauchy problem of the derivative Schrödinger equation in higher dimension is locally well-posed in H^(s)(R^(n))(s>n/2)for any large initial data.Thus this result can compare with that in one dimension except for the endpoint space H^(n/2).

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《数学年刊B辑（英文版）》 |2022年第6期|977-998|共22页
作者
Boling GUO; Zhaohui HUO;
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作者单位

Institute of Applied Physics and Computational Mathematics;

P.O.Box 8009;

Beijing 100088;

China;

Institute of Mathematics;

Academy of Mathematics and Systems Science;

CAS;

Beijing 100190;

China;

Hua Loo-Keng Key Laboratory of Mathematics;

Chinese Academy of Sciences;

Beijing 100190;

China;

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原文格式 PDF
正文语种 chi
中图分类非线性偏微分方程;
关键词
Well-posedness; Derivative Schrödinger equation in higher dimension; Short-time Xs; b; Large initial data;

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2. Long-time Asymptotic Behavior for the Derivative Schrödinger Equation with Finite Density Type Initial Data [J] . Yiling YANG ,Engui FAN . 数学年刊：B辑英文版 . 2022,第6期
3. On the well-posedness for stochastic fourth-order Schrdinger equations [J] . FANG Dao-yuan ZHANG Lin-zi ZHANG Ting . 高校应用数学学报：英文版（B辑） . 2011,第3期
4. A RIEMANN-HILBERT APPROACH TO THE INITIAL-BOUNDARY PROBLEM FOR DERIVATIVE NONLINEAR SCHRDINGER EQUATION [J] . 徐建 ,范恩贵 . 数学物理学报：B辑英文版 . 2014,第4期
5. 一类Schr?dinger方程的变分同化方法 [C] . 张瑰 ,刘希强 . 第29届中国气象学会年会 . 2012
6. Ground state solutions for coupled Schr(o)dinger systems and semiclassical solutions for quasilinear Schr(o)dinger equations [A] . Khine Min Min Oo . 2019

Local Well-posedness of the Derivative Schrödinger Equation in Higher Dimension for Any Large Data

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