The Schrodinger equation with singular time-dependent potentials

被引：1

作者：

Teismann, H ^{[1
]}

机构：

[1] N Dakota State Univ, Dept Math, Fargo, ND 58105 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2000年 / 6卷 / 03期

关键词：

Schrodinger equation; time-dependent potentials; evolution systems; well-posedness; Strichartz estimates; Lorentz spaces; fractional derivatives; generalized Sobolev spaces; generalized Leibnitz rule;

D O I：

10.3934/dcds.2000.6.705

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this note is to extend the theory of (linear) Schrodinger equations with time-dependent potentials developed by K. Yajima [29, 30] to slightly more singular potentials. This is done by proving that the well-known Strichartz estimates for the Schrodinger group remain valid if the usual Lebesgue spaces(1) are replaced by the Lorentz spaces L-p,L-2. Moreover, the regularity of the solutions can be described more precisely by utilizing a generalized Leibniz rule for fractional derivatives.

引用

页码：705 / 722

页数：18

共 31 条

[1]

[Anonymous], 1971, FOURIER ANAL EUCLIDE

[2]

Bergh J., 1976, INTERPOLATION SPACES

[3] Collision integrals for attractive potentials [J].