Long time dynamics of Yang-Mills-Higgs equations and applications

Abstract

The Yang-Mills-Higgs eqautions are the nonabelian generalization of Maxwell-Klein-Gordon system, which models the motion of charged particles in electromagnetic field. It is well known that such system admits global smooth solutions in general globally hyperbolic spacetimes. In this talk, we will show that the solutions in the future of a hyperboloid asymptotically decay like linear solutions for data bounded in some weighted energy space. The proof relies on vector field method and conformal invariance structure of the system. As applications, we also discuss the backward scattering problem with radiation data on the future null infinity.

Speaker

I am currently employed as Associate Professor at Beijing International Center for Mathematical Research in Peking University. I did my postdoc in University of Cambridge . My mentor there was Professor Mihalis Dafermos. I obtained my Ph.D in mathemtaics from Princeton University in June 2013 under the supervision of Professor Igor Rodnianski.