Low regularity for the nonlinear Klein-Gordon systems

Jia Yuan; Junyong Zhang

doi:10.1016/j.na.2008.01.026

Low regularity for the nonlinear Klein-Gordon systems

Jia Yuan, Junyong Zhang^*

^*Corresponding author for this work

China Academy of Engineering Physics

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

1 Citation (Scopus)

Abstract

In this paper, we study the global well-posedness below the energy norm of the Cauchy problem for the Klein-Gordon system in R³. We prove the H^s-global well-posedness with s < 1 of the Cauchy problem for the Klein-Gordon system. The method invoked is different from the well-known Bourgain's method [Jean Bourgain, Refinements of Strichartz's inequality and applications to 2D-NLS with critical nonlinearity, International Mathematial Research Notices 5 (1998) 253-283].

Original language	English
Pages (from-to)	982-998
Number of pages	17
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	70
Issue number	2
DOIs	https://doi.org/10.1016/j.na.2008.01.026
Publication status	Published - 15 Jan 2009
Externally published	Yes

Keywords

Bony's decomposition
Klein-Gordon equations system
Low regularity
Well-posedness

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10.1016/j.na.2008.01.026

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Yuan, J., & Zhang, J. (2009). Low regularity for the nonlinear Klein-Gordon systems. Nonlinear Analysis, Theory, Methods and Applications, 70(2), 982-998. https://doi.org/10.1016/j.na.2008.01.026

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AB - In this paper, we study the global well-posedness below the energy norm of the Cauchy problem for the Klein-Gordon system in R3. We prove the Hs-global well-posedness with s < 1 of the Cauchy problem for the Klein-Gordon system. The method invoked is different from the well-known Bourgain's method [Jean Bourgain, Refinements of Strichartz's inequality and applications to 2D-NLS with critical nonlinearity, International Mathematial Research Notices 5 (1998) 253-283].

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KW - Klein-Gordon equations system

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KW - Well-posedness

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IS - 2

ER -

Low regularity for the nonlinear Klein-Gordon systems

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Keywords

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