The Yang-Mills-Higgs Heat Flow on R3

The heat flow of the Yang-Mills-Higgs action functions on R3 is studied. It is found that if the Bogomolny tensor ∗ F − Dφ is initially small in certain p-norms, the heat flow exists for all time and converges to a monopole of the same magnetic charges as the initial configuration. This result, together with the approximate configurations constructed by C. Taubes (Comm. Math. Phys. 80, 1981, 343-367), yields an alternative proof of the existence of such solutions. The main technical tools used are the parabolic maximum principle and Sobolev and interpolation inequalities.