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

Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space PDF Author: Joachim Krieger
Publisher: American Mathematical Soc.
ISBN: 082184489X
Category : Mathematics
Languages : en
Pages : 111

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Book Description
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.