Endpoint Strichartz estimates for the Klein-Gordon equation in two space dimensions and some applications

Jun Kato; Tohru Ozawa

doi:10.1016/j.matpur.2010.10.001

Endpoint Strichartz estimates for the Klein-Gordon equation in two space dimensions and some applications

Jun Kato^*, Tohru Ozawa

^*Corresponding author for this work

School of Advanced Science and Engineering

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

10 Citations (Scopus)

Abstract

We prove the endpoint Strichartz estimates for the Klein-Gordon equation in mixed norms on the polar coordinates in two space dimensions. As an application, similar endpoint estimates for the Schrödinger equation in two space dimensions are shown by using the non-relativistic limit. The existence of global solutions for the cubic nonlinear Klein-Gordon equation in two space dimensions for small data is also shown.

Original language	English
Pages (from-to)	48-71
Number of pages	24
Journal	Journal des Mathematiques Pures et Appliquees
Volume	95
Issue number	1
DOIs	https://doi.org/10.1016/j.matpur.2010.10.001
Publication status	Published - 2011 Jan

Keywords

Angular regularity
Endpoint estimate
Klein-Gordon equation
Strichartz estimate

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1016/j.matpur.2010.10.001

Cite this

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title = "Endpoint Strichartz estimates for the Klein-Gordon equation in two space dimensions and some applications",

abstract = "We prove the endpoint Strichartz estimates for the Klein-Gordon equation in mixed norms on the polar coordinates in two space dimensions. As an application, similar endpoint estimates for the Schr{\"o}dinger equation in two space dimensions are shown by using the non-relativistic limit. The existence of global solutions for the cubic nonlinear Klein-Gordon equation in two space dimensions for small data is also shown.",

keywords = "Angular regularity, Endpoint estimate, Klein-Gordon equation, Strichartz estimate",

author = "Jun Kato and Tohru Ozawa",

year = "2011",

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doi = "10.1016/j.matpur.2010.10.001",

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AU - Kato, Jun

AU - Ozawa, Tohru

PY - 2011/1

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N2 - We prove the endpoint Strichartz estimates for the Klein-Gordon equation in mixed norms on the polar coordinates in two space dimensions. As an application, similar endpoint estimates for the Schrödinger equation in two space dimensions are shown by using the non-relativistic limit. The existence of global solutions for the cubic nonlinear Klein-Gordon equation in two space dimensions for small data is also shown.

AB - We prove the endpoint Strichartz estimates for the Klein-Gordon equation in mixed norms on the polar coordinates in two space dimensions. As an application, similar endpoint estimates for the Schrödinger equation in two space dimensions are shown by using the non-relativistic limit. The existence of global solutions for the cubic nonlinear Klein-Gordon equation in two space dimensions for small data is also shown.

KW - Angular regularity

KW - Endpoint estimate

KW - Klein-Gordon equation

KW - Strichartz estimate

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Endpoint Strichartz estimates for the Klein-Gordon equation in two space dimensions and some applications

Abstract

Keywords

ASJC Scopus subject areas

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