  We consider a nonlinear, spatially-nonlocal initial value problem in one
space dimension on $\mathbb{R}$ that describes the motion of surface
quasi-geostrophic (SQG) fronts. We prove that the initial value problem has a
unique local smooth solution under a convergence condition on the multilinear
expansion of the nonlinear term in the equation, and, for sufficiently smooth
and small initial data, we prove that the solution is global.
