Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space

Download or read book Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space written by Joachim Krieger and published by American Mathematical Soc.. This book was released on 2013-04-22 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 $\dot{H}_A^{(n-4)/{2}}$. 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 $L^p$ spaces, and also proving some bilinear estimates in specially constructed square-function spaces.