Willie Wong

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Electrical arc furnace (EAF), acting as a fast varying real power and reactive power sink, not only induces the power quality pollution back to utility, but also prevent the effective production of metal industry. In this paper, a methodology of designing an energy storage system (ESS) for EAFs is presented. Based on the field data-based study of a typical(More)
We introduce a suitable concept of weak evolution in the context of the radial quintic focussing semilinear wave equation on R3`1, that is adapted to continuation past type II singularities. We show that the weak extension leads to type I singularity formation for initial data corresponding to: (i) the Kenig-Merle blow-up solutions with initial energy below(More)
In this thesis, I study three problems related to the linear and nonlinear wave equations on black hole spacetimes. These problems are motivated by the nonlinear stability of Kerr spacetime. First, I prove that sufficiently regular solutions to the wave equation gΦ = 0 on the exterior of the Schwarzschild black hole obey the estimates |Φ| ≤ Cδ(t) 3 2 +δ and(More)
In this thesis, we propose a novel choice of gauge for the Yang-Mills equations on the Minkowski space R. A crucial ingredient is the associated Yang-Mills heat flow. Unlike the previous approaches (as in [15] and [33]), the new gauge is applicable for large data, while the special analytic structure of the Yang-Mills equations is still manifest. As the(More)
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