Local smoothing and Strichartz estimates for the Klein-Gordon equation with the inverse-square potential

Hyeongjin Lee; Ihyeok Seo; Jihyeon Seok

doi:10.3934/dcds.2020024

Local smoothing and Strichartz estimates for the Klein-Gordon equation with the inverse-square potential

Hyeongjin Lee, Ihyeok Seo, Jihyeon Seok

Department of Mathematics

Sungkyunkwan University

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

3 Scopus citations

Abstract

We prove weighted L² estimates for the Klein-Gordon equation perturbed with singular potentials such as the inverse-square potential. We then deduce the well-posedness of the Cauchy problem for this equation with small perturbations, and go on to discuss local smoothing and Strichartz estimates which improve previously known ones.

Original language	English
Pages (from-to)	597-608
Number of pages	12
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	40
Issue number	1
DOIs	https://doi.org/10.3934/dcds.2020024
State	Published - 2020

Keywords

Klein-Gordon equation
Smoothing estimates
Strichartz estimates

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title = "Local smoothing and Strichartz estimates for the Klein-Gordon equation with the inverse-square potential",

abstract = "We prove weighted L2 estimates for the Klein-Gordon equation perturbed with singular potentials such as the inverse-square potential. We then deduce the well-posedness of the Cauchy problem for this equation with small perturbations, and go on to discuss local smoothing and Strichartz estimates which improve previously known ones.",

keywords = "Klein-Gordon equation, Smoothing estimates, Strichartz estimates",

author = "Hyeongjin Lee and Ihyeok Seo and Jihyeon Seok",

year = "2020",

doi = "10.3934/dcds.2020024",

language = "English",

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pages = "597--608",

journal = "Discrete and Continuous Dynamical Systems- Series A",

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publisher = "American Institute of Mathematical Sciences",

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T1 - Local smoothing and Strichartz estimates for the Klein-Gordon equation with the inverse-square potential

AU - Lee, Hyeongjin

AU - Seo, Ihyeok

AU - Seok, Jihyeon

PY - 2020

Y1 - 2020

N2 - We prove weighted L2 estimates for the Klein-Gordon equation perturbed with singular potentials such as the inverse-square potential. We then deduce the well-posedness of the Cauchy problem for this equation with small perturbations, and go on to discuss local smoothing and Strichartz estimates which improve previously known ones.

AB - We prove weighted L2 estimates for the Klein-Gordon equation perturbed with singular potentials such as the inverse-square potential. We then deduce the well-posedness of the Cauchy problem for this equation with small perturbations, and go on to discuss local smoothing and Strichartz estimates which improve previously known ones.

KW - Klein-Gordon equation

KW - Smoothing estimates

KW - Strichartz estimates

UR - https://www.scopus.com/pages/publications/85074908045

U2 - 10.3934/dcds.2020024

DO - 10.3934/dcds.2020024

M3 - Article

AN - SCOPUS:85074908045

SN - 1078-0947

VL - 40

SP - 597

EP - 608

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 1

ER -

Local smoothing and Strichartz estimates for the Klein-Gordon equation with the inverse-square potential

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Keywords

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