The Yang-Mills heat equation with finite action in three dimensions / Leonard Gross.
Material type:
TextLanguage: English Series: ; V.275., No.1349. | Memoirs of the American Mathematical Society ; number 1349Publication details: USA : American Mathematical Society, c2022.Description: v, 111 pages ; 26 cmISBN: - 9781470450533
- 00659266
- 19476221
- Heat equation
- Yang-Mills theory
- Gauge fields (Physics)
- Partial differential equations -- Parabolic equations and systems -- Semilinear parabolic equations
- Partial differential equations -- Parabolic equations and systems -- Degenerate parabolic equations
- Mechanics of particles and systems -- Classical field theories -- Yang-Mills and other gauge theories
- Partial differential equations -- Parabolic equations and systems -- Initial-boundary value problems for second-order parabolic systems
- Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Heat and other parabolic equation methods
- Mathematics
- 515.353 23/eng20220503 GRO
- 35K58 | 35K65 | 70S15 | 35K51 | 58J35
| Item type | Current library | Collection | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|---|
Project book
|
CUTN Central Library Sciences | Non-fiction | 515.353 GRO (Browse shelf(Opens below)) | Checked out to Renuka Devi V (20019T) | 31/01/2024 | 48924 |
"January 2022, volume 275."
Includes bibliographical references.
Statement of results -- Solutions for the augmented Yang-Mills heat equation -- Initial behavior of solutions to the augmented equation -- Gauge groups -- The conversion group -- Recovery of A from C.
"The existence and uniqueness of solutions to the Yang-Mills heat equation is proven over R3 and over a bounded open convex set in R3. The initial data is taken to lie in the Sobolev space of order one half, which is the critical Sobolev index for this equation over a three dimensional manifold. The existence is proven by solving first an augmented, strictly parabolic equation and then gauge transforming the solution to a solution of the Yang-Mills heat equation itself. The gauge functions needed to carry out this procedure lie in the critical gauge group of Sobolev regularity three halves, which is a complete topological group in a natural metric but is not a Hilbert Lie group. The nature of this group must be understood in order to carry out the reconstruction procedure. Solutions to the Yang-Mills heat equation are shown to be strong solutions modulo these gauge functions. Energy inequalities and Neumann domination inequalities are used to establish needed initial behavior properties of solutions to the augmented equation"--
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