On some Schrödinger and wave equations with time dependent potentials

被引：0
作者：
Virginia Naibo
Atanas Stefanov
机构：
[1] Rose-Hulman Institute of Technology,Department of Mathematics
[2] University of Kansas,Department of Mathematics
来源：
Mathematische Annalen | 2006年 / 334卷
关键词：
Schrödinger equation; Wave equation; Strichartz estimates; 35Q55; 35J10; 35L05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The existence and uniqueness of solutions in the initial value problem for Schrödinger and wave equations in the presence of a (large) time dependent potential is studied. The usual Strichartz estimates for such linear evolutions are shown to hold true with optimal assumptions on the potentials. As a byproduct, one obtains a counterexample to the two dimensional double endpoint inhomogeneous Strichartz estimate.
引用
收藏
页码：325 / 338
页数：13
相关论文
共 21 条
[11]  
Klainerman undefined(3)undefined Invent. Math. 155 451-undefined
[12]  
Montgomery-Smith undefined(1993)undefined Internat. Math. Res. Notices no. 1 13-undefined
[13]  
Rodnianski undefined(1976)undefined Ann. Phys. (N.Y.) 97 279-undefined
[14]  
Ruiz undefined(6)undefined J. Math. Phys. 41 3523-undefined
[15]  
Simon undefined(3)undefined Duke Math. J. 55 699-undefined
[16]  
Simon undefined(1977)undefined Duke Math. J. 44 705-undefined
[17]  
Sjölin undefined(2000)undefined Partial Differential Equations 25 1471-undefined
[18]  
Strichartz undefined(4)undefined Proc. Amer. Math. Soc. 102 874-undefined
[19]  
Tao undefined(1987)undefined Comm. Math. Phys. 110 415-undefined
[20]  
Vega undefined(undefined)undefined undefined undefined undefined-undefined
123