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

Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space
Author :
Publisher : American Mathematical Soc.
Total Pages : 111
Release :
ISBN-10 : 9780821844892
ISBN-13 : 082184489X
Rating : 4/5 (92 Downloads)

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 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.


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