Finite energy local well-posedness for the Yang-Mills-Higgs equations in Lorenz gauge

Abstract

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.

16 pages

References in corpus (3)

• Finite energy global well-posedness of the Yang-Mills equations on ${\mathbb{R}}^{1+3}$: An approach using the Yang-Mills heat flow
• Gauge choice for the Yang-Mills equations using the Yang-Mills heat flow and local well-posedness in $H^1$
• Null structure and local well-posedness in the energy class for the Yang-Mills equations in Lorenz gauge