I will present recent results concerning global existence for the Kuramoto-Sivashinsky equation in 2 space dimensions with and without advection in the presence of growing modes. The KSE is a model of long-wave instability in dissipative systems, derived to describe flame-front propagation in combustion. This is joint work with David Ambrose (Drexel), Michele Coti-Zelati (Imperial College), Michele Dolce (EPFL), and Yuanyuan Feng (East China Normal University).