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March/April 2014 Low regularity local well-posedness for the Maxwell-Klein-Gordon equations in Lorenz gauge
Hartmut Pecher
Adv. Differential Equations 19(3/4): 359-386 (March/April 2014).

Abstract

The Cauchy problem for the Maxwell-Klein-Gordon equations in Lorenz gauge in two and three space dimensions is locally well-posed for low regularity data without finite energy. The result relies on the null structure for the main bilinear terms, which was shown to be not only present in Coulomb gauge but also in Lorenz gauge by Selberg and Tesfahun, who proved global well-posedness for finite energy data in three space dimensions. This null structure is combined with product estimates for wave-Sobolev spaces given systematically by d'Ancona, Foschi and Selberg.

Citation

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Hartmut Pecher. "Low regularity local well-posedness for the Maxwell-Klein-Gordon equations in Lorenz gauge." Adv. Differential Equations 19 (3/4) 359 - 386, March/April 2014.

Information

Published: March/April 2014
First available in Project Euclid: 30 January 2014

zbMATH: 1291.35304
MathSciNet: MR3161665

Subjects:
Primary: 35L70, 35Q61

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.19 • No. 3/4 • March/April 2014
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