Remarks on some dispersive estimates

Yonggeun Cho; Tohru Ozawa; Suxia Xia

doi:10.3934/cpaa.2011.10.1121

Remarks on some dispersive estimates

Yonggeun Cho^*, Tohru Ozawa, Suxia Xia

^*Corresponding author for this work

School of Advanced Science and Engineering

Research output: Contribution to journal › Article › peer-review

55 Citations (Scopus)

Abstract

In this paper we consider the initial value problem for i∂tu + ω(|r|)u = 0. Under suitable smoothness and growth conditions on ω, we derive dispersive estimates which is the generalization of time decay and Strichartz estimates. We unify and also simplify dispersive estimates by utilizing the Bessel function. Another main ingredient of this paper is to revisit oscillatory integrals of [2].

Original language	English
Pages (from-to)	1121-1128
Number of pages	8
Journal	Communications on Pure and Applied Analysis
Volume	10
Issue number	4
DOIs	https://doi.org/10.3934/cpaa.2011.10.1121
Publication status	Published - 2011 Jul

Keywords

Bessel functions
Dispersive equations
Dispersive estimate
Oscillatory integral
Strichartz estimate
Time decay

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.3934/cpaa.2011.10.1121

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author = "Yonggeun Cho and Tohru Ozawa and Suxia Xia",

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AB - In this paper we consider the initial value problem for i∂tu + ω(|r|)u = 0. Under suitable smoothness and growth conditions on ω, we derive dispersive estimates which is the generalization of time decay and Strichartz estimates. We unify and also simplify dispersive estimates by utilizing the Bessel function. Another main ingredient of this paper is to revisit oscillatory integrals of [2].

KW - Bessel functions

KW - Dispersive equations

KW - Dispersive estimate

KW - Oscillatory integral

KW - Strichartz estimate

KW - Time decay

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VL - 10

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EP - 1128

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 4

ER -

Remarks on some dispersive estimates

Abstract

Keywords

ASJC Scopus subject areas

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