Finite energy local well-posedness for the Yang–Mills–Higgs equations in Lorenz gauge
A Tesfahun - International Mathematics Research Notices, 2015 - academic.oup.com
International Mathematics Research Notices, 2015•academic.oup.com
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.
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.
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.
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