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

先進理工学部

研究成果: Article › 査読

4 被引用数 (Scopus)

抄録

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.

本文言語	English
ページ（範囲）	48-71
ページ数	24
ジャーナル	Journal des Mathematiques Pures et Appliquees
巻	95
号	1
DOI	https://doi.org/10.1016/j.matpur.2010.10.001
出版ステータス	Published - 2011 1

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1016/j.matpur.2010.10.001

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引用スタイル

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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",

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AU - Ozawa, Tohru

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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.

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KW - Endpoint estimate

KW - Klein-Gordon equation

KW - Strichartz estimate

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