  We consider the well-posedness of the generalized surface quasi-geostrophic
(gSQG) front equation. By using the null structure of the equation via a
paradifferential normal form analysis, we obtain balanced energy estimates,
which allow us to prove the local well-posedness of the non-periodic gSQG front
equation at a low level of regularity (in the SQG case, at only one-half
derivatives above scaling). In addition, we establish global well-posedness for
small and localized rough initial data, as well as modified scattering, by
using the testing by wave packet approach of Ifrim-Tataru.
