Compactness properties for geometric fourth order elliptic equations with application to the Q-curvature flow.

We prove the compactness of solutions of general fourth order elliptic equations which are L¹-perturbations of the Q-curvature equation on compact Riemannian 4-manifolds. Consequently, we prove the global existence and convergence of the Q-curvature flow on a generic class of Riemannian 4-manifolds. As a by-product, we give a positive answer to an open question by A. Malchiodi [12] on the existence of bounded Palais-Smale sequences for the Q-curvature problem when the Paneitz operator is positive with trivial kernel. [ABSTRACT FROM AUTHOR]