Table of Contents * Introduction * Some gauge-theoretic preliminaries * Reduction to the ""main a-priori estimate"" * Some analytic preliminaries * Proof of the main a-priori estimate * Reduction to approximate half-wave operators * Construction of the half-wave operators * Fixed time L2 estimates for the parametrix * The dispersive estimate * Decomposable function spaces and some applications * Completion of the proof * Bibliography.
(source: Nielsen Book Data)
This monograph contains a study of the global Cauchy problem for the Yang-Mills equations on (6 1) and higher dimensional Minkowski space, when the initial data sets are small in the critical gauge covariant Sobolev space H(n-4)/2A. Regularity is obtained through a certain ""microlocal geometric renormalization"" of the equations which is implemented via a family of approximate null Cronstrom gauge transformations. The argument is then reduced to controlling some degenerate elliptic equations in high index and non-isotropic Lp spaces, and also proving some bilinear estimates in specially constructed square-function spaces. (source: Nielsen Book Data)