Endpoint Strichartz estimates and global solutions for the nonlinear Dirac equation

Shuji Machihara, Makoto Nakamura, Kenji Nakanishi, Tohru Ozawa

Research output: Contribution to journalArticle

55 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 languageEnglish
Pages (from-to)1-20
Number of pages20
JournalJournal of Functional Analysis
Volume219
Issue number1
DOIs
Publication statusPublished - 2005 Feb 1
Externally publishedYes

Fingerprint

Strichartz Estimates
Global Well-posedness
Polar coordinates
Klein-Gordon Equation
Dirac Equation
Global Solution
Wave equation
Nonlinear Equations
Regularity
Norm
Energy
Class

Keywords

  • Endpoint Strichartz estimates
  • Klein-Gordon equation
  • Nonlinear Dirac equation

ASJC Scopus subject areas

  • Analysis

Cite this

Endpoint Strichartz estimates and global solutions for the nonlinear Dirac equation. / Machihara, Shuji; Nakamura, Makoto; Nakanishi, Kenji; Ozawa, Tohru.

In: Journal of Functional Analysis, Vol. 219, No. 1, 01.02.2005, p. 1-20.

Research output: Contribution to journalArticle

Machihara, Shuji ; Nakamura, Makoto ; Nakanishi, Kenji ; Ozawa, Tohru. / Endpoint Strichartz estimates and global solutions for the nonlinear Dirac equation. In: Journal of Functional Analysis. 2005 ; Vol. 219, No. 1. pp. 1-20.
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