Initial behavior of solutions to the Yang-Mills heat equation

@article{Charalambous2016InitialBO,
  title={Initial behavior of solutions to the Yang-Mills heat equation},
  author={Nelia Charalambous and Leonard Gross},
  journal={arXiv: Mathematical Physics},
  year={2016}
}
View PDF on arXiv
7 Citations

7 Citations

Stability of the Yang-Mills heat equation for finite action

The existence and uniqueness of solutions to the Yang-Mills heat equation over domains in Euclidean three space was proven in a previous paper for initial data lying in the Sobolev space of order…

The Yang-Mills heat equation with finite action in three dimensions

  • L. Gross
  • Mathematics
    Memoirs of the American Mathematical Society
  • 2022
The existence and uniqueness of solutions to the Yang-Mills heat equation is proven over R 3 \mathbb {R}^3 and over a bounded open convex set in R 3 \mathbb {R}^3…

A Functional Integral Approaches to the Makeenko–Migdal Equations

  • B. Driver
  • Mathematics
    Communications in Mathematical Physics
  • 2019
Makeenko and Migdal (Phys Lett B 88(1):135–137, 1979) gave heuristic identities involving the expectation of the product of two Wilson loop functionals associated to splitting a single loop at a…

Equivalence of helicity and Euclidean self-duality for gauge fields

  • L. Gross
  • Mathematics
    Nuclear Physics B
  • 2019

The Yang-Mills Heat Equation on Three-Manifolds with Boundary

In this short note we provide an expository account of the work of Leonard Gross and the author on the Yang-Mills heat equation over smooth three-manifolds with boundary.

The Yang-Mills heat flow with random distributional initial data

  • Sky CaoS. Chatterjee
  • Mathematics, Computer Science
    Communications in Partial Differential Equations
  • 2023
The main idea, which goes back to work of Bourgain as well as work of Da Prato-Debussche, is to decompose the solution into a rougher linear part and a smoother nonlinear part and to control the latter by probabilistic arguments.

Yang–Mills for Probabilists

  • S. Chatterjee
  • Mathematics
    Probability and Analysis in Interacting Physical Systems
  • 2019
The rigorous construction of quantum Yang-Mills theories, especially in dimension four, is one of the central open problems of mathematical physics. Construction of Euclidean Yang-Mills theories is…

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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…

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Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued…

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Abstract. We develop the existence and regularity theory for the generalized Neumann problem for Yang-Mills connections. This is the most general boundary value problem for connections on a compact…

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The purpose of this paper is defining a new boundary value problem for Yang-Mills connections, which is the most general in the context of Neumann-type problems for forms. We achieve this by…

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