### 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 Ḣ^{n/2-1} × Ḣ^{n/2-2} 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.

Original language | English (US) |
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Pages (from-to) | 377-426 |

Number of pages | 50 |

Journal | Communications In Mathematical Physics |

Volume | 251 |

Issue number | 2 |

DOIs | |

State | Published - Nov 1 2004 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics