Finite Energy Local Well-Posedness for the Yang-Mills-Higgs Equations in Lorenz Gauge

The Yang-Mills-Higgs equations (Y-M-H), when written relative to Lorenz gauge, become a system of nonlinear wave equations. The key bilinear terms in the resulting system turn out to be null forms-this is in light of a recent discovery of null structure by Selberg and the present author for Yang-Mills equations in Lorenz gauge. Using the null structure found and bilinear space-time estimates, we prove local well-posedness of Y-M-H in Lorenz gauge for finite energy data.