一类非椭圆薛定谔方程的Cauchy问题的光滑性效应

SMOOTHING EFFECT OF CAUCHY PROBLEM FOR A CLASSOF NON-ELLIPTIC SCHRODINGER EQUATION

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了估计,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.

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 Schrodinger 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 Schrodinger equation.