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.
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页码：705 / 722
页数：18
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