Communications in Mathematical Physics

, Volume 251, Issue 2, pp 377–426

Global Regularity for the Maxwell-Klein-Gordon Equation with Small Critical Sobolev Norm in High Dimensions

Article

DOI: 10.1007/s00220-004-1152-1

Cite this article as:
Rodnianski, I. & Tao, T. Commun. Math. Phys. (2004) 251: 377. doi:10.1007/s00220-004-1152-1

Abstract.

We show that in dimensions n ≥ 6 one has global regularity for the Maxwell-Klein-Gordon equations in the Coulomb gauge provided that the critical Sobolev norm https://static-content.springer.com/image/art%3A10.1007%2Fs00220-004-1152-1/MediaObjects/s00220-004-1152-1flb1.gif of the initial data is sufficiently small. These results are analogous to those recently obtained for the high-dimensional wave map equation [17, 7, 14, 12] but unlike the wave map equation, the Coulomb gauge non-linearity cannot be iterated away directly. We shall use a different approach, proving Strichartz estimates for the covariant wave equation. This in turn will be achieved by use of Littlewood-Paley multipliers, and a global parametrix for the covariant wave equation constructed using a truncated, microlocalized Cronstrom gauge.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Department of MathematicsUCLALos AngelesUSA