Duke Mathematical Journal

Global well-posedness for the Maxwell–Klein–Gordon equation in 4+1 dimensions: Small energy

Joachim Krieger, Jacob Sterbenz, and Daniel Tataru

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Abstract

We prove that the critical Maxwell–Klein–Gordon equation on R4+1 is globally well-posed for smooth initial data which are small in the energy norm. This reduces the problem of global regularity for large, smooth initial data to precluding concentration of energy.

Article information

Source
Duke Math. J., Volume 164, Number 6 (2015), 973-1040.

Dates
First available in Project Euclid: 17 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1429282677

Digital Object Identifier
doi:10.1215/00127094-2885982

Mathematical Reviews number (MathSciNet)
MR3336839

Zentralblatt MATH identifier
1329.35209

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 70S15: Yang-Mills and other gauge theories

Keywords
critical MKG critical dispersive equations global well-posedness

Citation

Krieger, Joachim; Sterbenz, Jacob; Tataru, Daniel. Global well-posedness for the Maxwell–Klein–Gordon equation in $4+1$ dimensions: Small energy. Duke Math. J. 164 (2015), no. 6, 973--1040. doi:10.1215/00127094-2885982. https://projecteuclid.org/euclid.dmj/1429282677


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