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

Department of Mathematics

Waseda University
Beihang University

Research output: Contribution to journal › Journal article › peer-review

74 Scopus citations

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
State	Published - 2011.07

Keywords

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

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.3934/cpaa.2011.10.1121

Cite this

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title = "Remarks on some dispersive estimates",

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].",

keywords = "Bessel functions, Dispersive equations, Dispersive estimate, Oscillatory integral, Strichartz estimate, Time decay",

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

year = "2011",

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doi = "10.3934/cpaa.2011.10.1121",

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pages = "1121--1128",

journal = "Communications on Pure and Applied Analysis",

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T1 - Remarks on some dispersive estimates

AU - Cho, Yonggeun

AU - Ozawa, Tohru

AU - Xia, Suxia

PY - 2011/7

Y1 - 2011/7

N2 - 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].

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

UR - https://www.scopus.com/pages/publications/82155191489

U2 - 10.3934/cpaa.2011.10.1121

DO - 10.3934/cpaa.2011.10.1121

M3 - Journal article

AN - SCOPUS:82155191489

SN - 1534-0392

VL - 10

SP - 1121

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

Quacquarelli Symonds(QS) Subject Topics

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