Endpoint Strichartz estimates and global solutions for the nonlinear Dirac equation

Shuji Machihara; Makoto Nakamura; Kenji Nakanishi; Tohru Ozawa

doi:10.1016/j.jfa.2004.07.005

Endpoint Strichartz estimates and global solutions for the nonlinear Dirac equation

Shuji Machihara, Makoto Nakamura, Kenji Nakanishi, Tohru Ozawa

School of Advanced Science and Engineering

Research output: Contribution to journal › Article

56 Citations (Scopus)

Abstract

We prove endpoint Strichartz estimates for the Klein-Gordon and wave equations in mixed norms on the polar coordinates in three spatial dimensions. As an application, global wellposedness of the nonlinear Dirac equation is shown for small data in the energy class with some regularity assumption for the angular variable.

Original language	English
Pages (from-to)	1-20
Number of pages	20
Journal	Journal of Functional Analysis
Volume	219
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2004.07.005
Publication status	Published - 2005 Feb 1

Keywords

Endpoint Strichartz estimates
Klein-Gordon equation
Nonlinear Dirac equation

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2004.07.005

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title = "Endpoint Strichartz estimates and global solutions for the nonlinear Dirac equation",

abstract = "We prove endpoint Strichartz estimates for the Klein-Gordon and wave equations in mixed norms on the polar coordinates in three spatial dimensions. As an application, global wellposedness of the nonlinear Dirac equation is shown for small data in the energy class with some regularity assumption for the angular variable.",

keywords = "Endpoint Strichartz estimates, Klein-Gordon equation, Nonlinear Dirac equation",

author = "Shuji Machihara and Makoto Nakamura and Kenji Nakanishi and Tohru Ozawa",

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AU - Machihara, Shuji

AU - Nakamura, Makoto

AU - Nakanishi, Kenji

AU - Ozawa, Tohru

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Y1 - 2005/2/1

N2 - We prove endpoint Strichartz estimates for the Klein-Gordon and wave equations in mixed norms on the polar coordinates in three spatial dimensions. As an application, global wellposedness of the nonlinear Dirac equation is shown for small data in the energy class with some regularity assumption for the angular variable.

AB - We prove endpoint Strichartz estimates for the Klein-Gordon and wave equations in mixed norms on the polar coordinates in three spatial dimensions. As an application, global wellposedness of the nonlinear Dirac equation is shown for small data in the energy class with some regularity assumption for the angular variable.

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KW - Klein-Gordon equation

KW - Nonlinear Dirac equation

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