  We consider a closed surface in $\mathbb{R}^3$ evolving by the
volume-preserving Willmore flow and prove a lower bound for the existence time
of smooth solutions. For spherical initial surfaces with Willmore energy below
$8\pi$ we show long time existence and convergence to a round sphere by
performing a suitable blow-up and by proving a constrained Lojasiewicz-Simon
inequality.
