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

页码：325 / 338

页数：13

共 21 条

[1]

Constantin V.(2)Decay estimates for the wave equation with potential J. Amer. Math. Soc. 1 413-1369

[2]

Georgiev N.(2003)Well-posedness and local smoothing of solutions of Schrödinger equations Comm. Partial Diff. Equations 28 1325-205

[3]

Visciglia A.(1989)Spherically averaged end point Strichartz estimates for the two-dimensional Schrödinger equation, Comm Comm. Math. Phys. 123 535-1485

[4]

Ginibre C.(1)undefined Comm. Math. Phys. 251 157-undefined

[5]

Goldberg T.(2005)undefined Math. Res. Lett. 12 193-undefined

[6]

Ionescu undefined(2)undefined J. Math. Soc. Japan 47 253-undefined

[7]

Kenig undefined(1998)undefined Amer. J. Math. 120 955-undefined

[8]

Jensen undefined(3)undefined Invent. Math. 134 489-undefined

[9]

Keel undefined(1993)undefined Comm. Pure Appl. Math. 46 1221-undefined

[10]

Kenig undefined(2)undefined Duke Math. J. 91 393-undefined

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