Local well-posedness for the Klein-Gordon-Zakharov system in 3D

Hartmut Pecher

doi:10.3934/dcds.2020338

Article Contents

2021, Volume 41, Issue 4: 1707-1736. Doi: 10.3934/dcds.2020338

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Local well-posedness for the Klein-Gordon-Zakharov system in 3D

Hartmut Pecher

Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany

Received: April 30, 2020

Revised: July 31, 2020

Early access: October 2020

Published: April 2021

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Abstract

We study the Cauchy problem for the Klein-Gordon-Zakharov system in 3D with low regularity data. We lower down the regularity to the critical value with respect to scaling up to the endpoint. The decisive bilinear estimates are proved by means of methods developed by Bejenaru-Herr for the Zakharov system and already applied by Kinoshita to the Klein-Gordon-Zakharov system in 2D.

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Mathematics Subject Classification: 35Q55, 35A01.

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References

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