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| 摘要: |
| 本文研究了流体力学中用于描述弱非线性水波的Davey-Stewartson系统的一种特殊情况，即一类齐次非椭圆薛定谔方程的柯西问题.利用傅里叶分析以及交换子估计，证明了这一类方程具有光滑效应，推广了经典薛定谔方程的类似结果. |
| 关键词: 薛定谔方程 光滑效应 交换子 |
| DOI： |
| 分类号:O175.23 |
| 基金项目:国家自然科学基金资助（12031006）. |
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| SMOOTHING EFFECT OF CAUCHY PROBLEM FOR A CLASS OF NON-ELLIPTIC SCHRÖDINGER EQUATION |
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CAO Xiao-dong,GUO Liu-tao
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| Abstract: |
| In this paper, we work on a special case of Davey-Stewartson systems which is used to describe weakly nonlinear water waves in fluid mechanics, which is the Cauchy problem for a class of homogeneous non-elliptic Schrödinger equation. By using Fourier analysis and estimates for commutator bracket, we obtain this class of equation has smoothing effect, which generalizes some similar results of the classical Schrödinger equation. |
| Key words: Schrö dinger equation smoothing effect commutator bracket |
