  We consider the Kuramoto-Sivashinsky equation (KSE) on the two-dimensional
torus in the presence of advection by a given background shear flow. Under the
assumption that the shear has a finite number of critical points and there are
linearly growing modes only in the direction of the shear, we prove global
existence of solutions with data in $L^2$, using a bootstrap argument. The
initial data can be taken arbitrarily large.
