Advances in Differential Equations

Low regularity local well-posedness for the Maxwell-Klein-Gordon equations in Lorenz gauge

Hartmut Pecher

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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.

Article information

Source
Adv. Differential Equations Volume 19, Number 3/4 (2014), 359-386.

Dates
First available in Project Euclid: 30 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.ade/1391109089

Mathematical Reviews number (MathSciNet)
MR3161665

Zentralblatt MATH identifier
1291.35304

Subjects
Primary: 35Q61: Maxwell equations 35L70: Nonlinear second-order hyperbolic equations

Citation

Pecher, Hartmut. Low regularity local well-posedness for the Maxwell-Klein-Gordon equations in Lorenz gauge. Adv. Differential Equations 19 (2014), no. 3/4, 359--386. https://projecteuclid.org/euclid.ade/1391109089.


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