**Memoirs of the American Mathematical Society**

2013;
99 pp;
Softcover

MSC: Primary 35;
Secondary 70

Print ISBN: 978-0-8218-4489-2

Product Code: MEMO/223/1047

List Price: $69.00

AMS Member Price: $41.40

MAA Member Price: $62.10

**Electronic ISBN: 978-0-8218-9871-0
Product Code: MEMO/223/1047.E**

List Price: $69.00

AMS Member Price: $41.40

MAA Member Price: $62.10

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

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*Joachim Krieger; Jacob Sterbenz*

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 Crönstrom 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.

#### Table of Contents

# Table of Contents

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

- Chapter 1. Introduction 18 free
- Chapter 2. Some Gauge-Theoretic Preliminaries 714
- Chapter 3. Reduction to the “Main a-Priori Estimate” 1320
- Chapter 4. Some Analytic Preliminaries 2532
- Chapter 5. Proof of the Main A-Priori Estimate 3138
- Chapter 6. Reduction to Approximate Half-Wave Operators 3946
- Chapter 7. Construction of the Half-Wave Operators 4350
- Chapter 8. Fixed Time 𝐿² Estimates for the Parametrix 4956
- Chapter 9. The Dispersive Estimate 7784
- Chapter 10. Decomposable Function Spaces and Some Applications 8188
- Chapter 11. Completion of the Proof 93100
- Bibliography 99106