## Analysis & PDE

• Anal. PDE
• Volume 9, Number 8 (2016), 1829-1902.

### Decay of solutions of Maxwell–Klein–Gordon equations with arbitrary Maxwell field

Shiwu Yang

#### Abstract

In the author’s previous work, it has been shown that solutions of Maxwell–Klein–Gordon equations in $ℝ3+1$ possess some form of global strong decay properties with data bounded in some weighted energy space. In this paper, we prove pointwise decay estimates for the solutions for the case when the initial data are merely small on the scalar field but can be arbitrarily large on the Maxwell field. This extends the previous result of Lindblad and Sterbenz, in which smallness was assumed both for the scalar field and the Maxwell field.

#### Article information

Source
Anal. PDE, Volume 9, Number 8 (2016), 1829-1902.

Dates
Revised: 7 March 2016
Accepted: 28 August 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.apde/1510843377

Digital Object Identifier
doi:10.2140/apde.2016.9.1829

Mathematical Reviews number (MathSciNet)
MR3599520

Zentralblatt MATH identifier
1358.35184

Subjects
Primary: 35Q61: Maxwell equations

Keywords
Maxwell–Klein–Gordon decay

#### Citation

Yang, Shiwu. Decay of solutions of Maxwell–Klein–Gordon equations with arbitrary Maxwell field. Anal. PDE 9 (2016), no. 8, 1829--1902. doi:10.2140/apde.2016.9.1829. https://projecteuclid.org/euclid.apde/1510843377

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