| eBook ISBN: | 978-0-8218-9871-0 |
| Product Code: | MEMO/223/1047.E |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $41.40 |
| eBook ISBN: | 978-0-8218-9871-0 |
| Product Code: | MEMO/223/1047.E |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $41.40 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 223; 2013; 99 ppMSC: Primary 35; Secondary 70
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.
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Table of Contents
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Chapters
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1. Introduction
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2. Some Gauge-Theoretic Preliminaries
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3. Reduction to the “Main a-Priori Estimate”
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4. Some Analytic Preliminaries
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5. Proof of the Main A-Priori Estimate
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6. Reduction to Approximate Half-Wave Operators
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7. Construction of the Half-Wave Operators
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8. Fixed Time $L^2$ Estimates for the Parametrix
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9. The Dispersive Estimate
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10. Decomposable Function Spaces and Some Applications
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11. Completion of the Proof
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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 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.
-
Chapters
-
1. Introduction
-
2. Some Gauge-Theoretic Preliminaries
-
3. Reduction to the “Main a-Priori Estimate”
-
4. Some Analytic Preliminaries
-
5. Proof of the Main A-Priori Estimate
-
6. Reduction to Approximate Half-Wave Operators
-
7. Construction of the Half-Wave Operators
-
8. Fixed Time $L^2$ Estimates for the Parametrix
-
9. The Dispersive Estimate
-
10. Decomposable Function Spaces and Some Applications
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11. Completion of the Proof
