Author : Joachim Krieger
Release : 2013-04-22
Genre : Mathematics
Kind : eBook
Book Rating : 89X/5 ( reviews)
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Book Synopsis Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space by : Joachim Krieger
Download or read book Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space written by Joachim Krieger. This book was released on 2013-04-22. 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.