Advances in Differential Equations
- Adv. Differential Equations
- Volume 19, Number 3/4 (2014), 359-386.
Low regularity local well-posedness for the Maxwell-Klein-Gordon equations in Lorenz gauge
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.
Adv. Differential Equations, Volume 19, Number 3/4 (2014), 359-386.
First available in Project Euclid: 30 January 2014
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q61: Maxwell equations 35L70: Nonlinear second-order hyperbolic equations
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