THE GLOBAL EXISTENCE AND DECAY ESTIMATES OF MAXWELL HIGGS THEORY IN FOUR DIMENSIONS - Mulyanto
In this dissertation, the interaction of complex scalar field and electromagnetic field (Maxwell-Higgs system) on four-dimensional spacetime is considered. In the first part, the global existence of Maxwell-Higgs theory with generalised gauge coupling with the addition of scalar potential in Minkowski spacetime is investigated. By taking the Kähler potential bounded by U(1)N symmetric Kähler potential, the gauge coupling which is a bounded function, and the scalar potential in the form of polynomial, sine-Gordon, or Toda potential, the global existence of this system is proved. In the second part, the decay estimates of the Maxwell-Higgs system in four-dimensional Schwarzschild space are proved. It is shown that if the field equations support Morawetz-type estimates, then uniform decay properties around the outside of the Schwarzschild black hole can be obtained using the Sobolev inequality and its energy estimates. The results also consider various forms of physical potential as in the first part.