Heat flow of Yang-Mills-Higgs functionals in dimension two

Abstract

We consider the heat flow of Yang-Mills-Higgs functional where the base manifold is a Riemannian surface and the fiber is a compact symplectic manifold. We show that the corresponding Cauchy problem admits a global weak solution for any $H^1$-initial data. Moreover, the solution is smooth except finitely many singularities. We prove an energy identity at finite time singularities and give a description of the asymptotic behavior at time infinity.