  In this paper, we establish that: Suppose a closed Riemannian manifold
$(M^n,g_0)$ of dimension $\geq 8$ is not locally conformally flat, then the
Paneitz-Sobolev constant of $M^n$ has the property that $q(g_0)<q(S^n)$. The
analogy of this result was obtained by T. Aubin in 1976 and had been used to
solve the Yamabe problem on closed manifolds. As an application, the above
result can be used to recover the sequential convergence of the nonlocal
Q-curvature flow on closed manifolds recently introduced by Gursky-Malchiodi.
