Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in 2D

Shinya Kinoshita

doi:10.3934/dcds.2018061

Article Contents

2018, Volume 38, Issue 3: 1479-1504. Doi: 10.3934/dcds.2018061

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Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in 2D

Shinya Kinoshita

Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan

Received: April 30, 2017

Revised: September 30, 2017

Published: June 2018

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Abstract

This paper is concerned with the Cauchy problem of the Klein-Gordon-Zakharov system with very low regularity initial data. We prove the bilinear estimates which are crucial to get the local in time well-posedness. The estimates are established by the Fourier restriction norm method. We utilize the nonlinear version of the classical Loomis-Whitney inequality.

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Mathematics Subject Classification: 35Q55, 35A01.

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References

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