Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space
Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space (Memoirs of the American Mathematical Society) by Joachim Krieger, Jacob Sterbenz
2013 | ISBN: 082184489X | English | 99 pages | PDF | 1 MB
2013 | ISBN: 082184489X | English | 99 pages | PDF | 1 MB
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.