On the optimal local regularity for gauge field theories (Q1979017)

The authors present the main estimates which allow to prove local well-posedness in \(H^s\), \(s>(n-2)/2\), in the case of the Maxwell-Klein-Gordon equations in \(n+1\) dimensions, \(n\geq 4\). For simplicity the relevance of these estimates is demonstrated for a model problem which exhibits all the main difficulties encountered in the Maxwell-Klein-Gordon equations relative to the Coulomb gauge.