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Mathematical Physics

arXiv:1405.6496 (math-ph)
[Submitted on 26 May 2014 (v1), last revised 30 May 2014 (this version, v2)]

Title:Neumann domination for the Yang-Mills heat equation

Authors:Nelia Charalambous, Leonard Gross
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Abstract:Long time existence and uniqueness of solutions to the Yang-Mills heat equation have been proven over a compact 3-manifold with boundary for initial data of finite energy. In the present paper we improve on previous estimates by using a Neumann domination technique that allows us to get much better pointwise bounds on the magnetic field. As in the earlier work, we focus on Dirichlet, Neumann and Marini boundary conditions. In addition, we show that the Wilson Loop functions, gauge invariantly regularized, converge as the parabolic time goes to infinity.
Comments: Correction in references from earlier version
Subjects: Mathematical Physics (math-ph); Analysis of PDEs (math.AP)
MSC classes: Primary, 35K58, 35K65, Secondary, 70S15, 35K51, 58J35
Cite as: arXiv:1405.6496 [math-ph]
  (or arXiv:1405.6496v2 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1405.6496

Submission history

From: Nelia Charalambous [view email]
[v1] Mon, 26 May 2014 08:12:13 UTC (46 KB)
[v2] Fri, 30 May 2014 05:46:28 UTC (46 KB)
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