Global Regularity For The Yang Mills Equations On High Dimensional Minkowski Space
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Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space
Author | : Joachim Krieger |
Publisher | : American Mathematical Soc. |
Total Pages | : 111 |
Release | : 2013-04-22 |
Genre | : Mathematics |
ISBN | : 082184489X |
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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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