Event № 839
The gauge theoretic format with a nonabelian bundle was first introduced by Mills and Yang in 1954 to model the strong and weak interactions in the nucleus of a particle. The Yang-Mills heat equation is the gradient flow corresponding to the Yang-Mills functional in this setting. It is a nonlinear weakly parabolic equation whose solutions can blow-up in finite time depending on the dimension. We will consider this equation over compact three-manifolds with boundary, and illustrate how one can prove long-time existence and uniqueness of strong solutions by gauge symmetry breaking. We will also demonstrate some strong regularization results for the solution and see how they lead to detailed short-time asymptotic estimates, as well as the long-time convergence of the Wilson loop functions.