Dispersive and Strichartz estimates for the three-dimensional wave equation with a scaling-critical class of potentials

The Anh Bui; Xuan Thinh Duong; Younghun Hong

doi:10.1016/j.jfa.2016.06.020

Dispersive and Strichartz estimates for the three-dimensional wave equation with a scaling-critical class of potentials

The Anh Bui, Xuan Thinh Duong, Younghun Hong^*

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

We consider the three-dimensional linear wave equation perturbed by a potential V belonging to a scaling-critical class which is the closure of bounded, compactly supported functions with respect to the global Kato norm. Without any further smallness assumptions, we first prove the dispersive estimate for the solution of the wave equation. As a byproduct, we prove Strichartz estimates under a slightly stronger condition.

Original language	English
Pages (from-to)	2215-2246
Number of pages	32
Journal	Journal of Functional Analysis
Volume	271
Issue number	8
DOIs	https://doi.org/10.1016/j.jfa.2016.06.020
Publication status	Published - 15 Oct 2016

Keywords

Besov space
Dispersive estimate
Kato potential
Wave equation

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10.1016/j.jfa.2016.06.020

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title = "Dispersive and Strichartz estimates for the three-dimensional wave equation with a scaling-critical class of potentials",

abstract = "We consider the three-dimensional linear wave equation perturbed by a potential V belonging to a scaling-critical class which is the closure of bounded, compactly supported functions with respect to the global Kato norm. Without any further smallness assumptions, we first prove the dispersive estimate for the solution of the wave equation. As a byproduct, we prove Strichartz estimates under a slightly stronger condition.",

keywords = "Besov space, Dispersive estimate, Kato potential, Wave equation",

author = "Bui, {The Anh} and Duong, {Xuan Thinh} and Younghun Hong",

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T1 - Dispersive and Strichartz estimates for the three-dimensional wave equation with a scaling-critical class of potentials

AU - Bui, The Anh

AU - Duong, Xuan Thinh

AU - Hong, Younghun

PY - 2016/10/15

Y1 - 2016/10/15

N2 - We consider the three-dimensional linear wave equation perturbed by a potential V belonging to a scaling-critical class which is the closure of bounded, compactly supported functions with respect to the global Kato norm. Without any further smallness assumptions, we first prove the dispersive estimate for the solution of the wave equation. As a byproduct, we prove Strichartz estimates under a slightly stronger condition.

AB - We consider the three-dimensional linear wave equation perturbed by a potential V belonging to a scaling-critical class which is the closure of bounded, compactly supported functions with respect to the global Kato norm. Without any further smallness assumptions, we first prove the dispersive estimate for the solution of the wave equation. As a byproduct, we prove Strichartz estimates under a slightly stronger condition.

KW - Besov space

KW - Dispersive estimate

KW - Kato potential

KW - Wave equation

UR - http://www.scopus.com/inward/record.url?scp=84995577356&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/DP140100649

U2 - 10.1016/j.jfa.2016.06.020

DO - 10.1016/j.jfa.2016.06.020

M3 - Article

AN - SCOPUS:84995577356

SN - 0022-1236

VL - 271

SP - 2215

EP - 2246

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 8

ER -

Dispersive and Strichartz estimates for the three-dimensional wave equation with a scaling-critical class of potentials

Abstract

Keywords

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Harmonic Analysis and Partial Differential Operators

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Dispersive and Strichartz estimates for the three-dimensional wave equation with a scaling-critical class of potentials

Abstract

Keywords

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Harmonic Analysis and Partial Differential Operators

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