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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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.

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

First available in Project Euclid: 17 April 2015

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Zentralblatt MATH identifier

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

critical MKG critical dispersive equations global well-posedness


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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